It looks like I'm not going to get anywhere on this, and I'll let it go.  But as a final point of clarification, I don't especially care about the xref.  My issue is that I *really* don't think "reference" or "referral" are appropriate glosses here.  They aren't generically useful outside of a few idiomatic expressions, and I find them particularly misleading.

I don't think they are close enough to justify an xref. None of the JE entries for 照会 suggest 問い合わせ as a synonym.

https://www.robertwalters.co.jp/career-advice/reference-check.html
リファレンスチェックとは
リファレンスチェックは、英語では「Reference Check」、身元照会という意味になります。

https://ja.wikipedia.org/wiki/信用照会
信用照会 = [credit card] (pre) authorization.   We're not going to add "authorization" as a gloss here just to handle this case, I take it:
信用照会	4629

I just read up on every edit I've made since November. I appreciate all of the work in checking updates, and the discussions were all interesting to catch up on.

As a prelude to this comment, I've proposed an entry for 身元照会, which I would argue is idiomatic("reference check").  Even putting "reference" in this entry doesn't fix that entry.

Anyway, of everything since November, this one entry I still disagree on.  A question was asked: "why is there an xref to 問い合わせ, they aren't the same..." The sankoku defn. of 照会 is:
1. [名・他さ]問い合わせ（ること）。「手紙でーする」

That's it.

Granting that sankoku is not the be-all-end-all of the Japanese language, you don't get much more "exactly the same" than that.  It just seems like we're reading something "special" into this term that isn't really there, perhaps because of some GG5 glosses.

身元の照会/身元照会 is not a good counterexample.  It is a completely idiomatic expression. "inquiry into one's work history/past" = "reference check".  身元照会先 "person to whom one inquires to gain information about an applicant's background history" = (job) reference.  1-word translation.  The lumine example given:

ルミナス: 詳しい情報については支配人に照会するように言われた I was referred to the manager for detailed information.
is literally "I was told to ask the manager".

照会する is not "refer" here.  "照会するように言われる" is "to be referred".  You need the whole thing. "To be told to ask someone else" = "refer".　

On top of that, there is a homonym 紹介, which *literally* means "introduction" or "referral" in the sense that we usually expect(referral from a doctor).  This even leads to mistakes in Japanese (some of which I pointed out in my treatise).  

The presence of "reference" is doubly-misleading because of the adjacent entry "照会先" "job reference", which really makes this term look like something it isn't.

And then we have the related-kanji term 参照, which literally means "reference" as in "research material".  Same kanji, same gloss, that makes these terms look potentially synonymous, and they aren't at all.

Having "reference" and "referral" here muddies the waters for very little gain.  This is a statement from experience, as I'm still untangling this vocabulary in my head.  

Almost any argument you could make for including "reference" or "referral" here could be made for adding them to 問い合わせ.  For example, here's the lumine example:
問い合わせるように	2563	92.9%
照会するように	196	7.1%

https://ejje.weblio.jp/content/問い合わせる
詳しいことについては秘書に問い合わせるように言われた.
I was referred to the secretary for detailed information.

Would it not be silly to add "reference" to 問い合わせ for that?  This is precisely why I put the xref in, as a means of saying "hey, these really are almost exactly the same".

I agree wrt the xref.

Not identical in meaning to 問い合わせ - not seeing the point of the xref.

@@ -20 +19,0 @@
-<xref type="see" seq="1598590">問い合わせ</xref>

GG5: 	(an) inquiry; (an) enquiry; (a) reference; (a) referral.
 ～する  ... refer [make a reference] to 《sb for sth》  ...
身元の照会 a background reference
ルミナス: 詳しい情報については支配人に照会するように言われた I was referred to the manager for detailed information.

While they are less common, I think reference and referral should be included.

@@ -23,0 +24,2 @@
+<gloss>reference</gloss>
+<gloss>referral</gloss>

Rough numbers (reverso clearly estimates)
https://context.reverso.net/translation/japanese-english/照会
inquiry: 1057
query:1053
inquire:113
enquiry: 30
referral: 29

問い合わせ	168990809	85.9%
問合せ	24497913	12.5%
照会	3198059	1.6%
照会先	14741	0.0%

"(credit) reference agency"
信用照会機関	56	24.2%
照会機関	175	75.8%

daijs: ［名］(スル)問い合わせて確かめること

From reverso: A nice looking "inquire" = "refer" alignment: ("you can inquire at...")
JMBパスワードがお分かりにならない場合はJALホームページで照会が可能です。
Please refer to the JAL website if you forgot your JMB PIN.

Here is a case where you *might* choose to gloss this as refer (but it still means "inquire"):
https://eow.alc.co.jp/search?q=照会
（人）の信用状態についてX銀行に照会する
refer to the X bank for someone's credit standing

With 先 = reference
（人）を～に推薦するために照会先となる
be a reference for someone's nomination to

Probable eijiro mistake about medical referrals. Gloss differs from example sentence, this looks like jumbled-up kanji:
https://eow.alc.co.jp/search?q=referral&ref=awlj
〔専門医などへの〕照会、委託
・My doctor gave me a referral to a knee specialist. : 私のかかりつけ医は、私に膝の専門家を紹介してくれました。

eijiro: referral service
照会［紹介］サービス
照会サービス	21808	9.6%  <-- is this a synonym, or something else though? Looks like something else (below)
紹介サービス	206475	90.4%

ETC 照会サービス (Japanese toll system ETC)
https://www.etc-meisai.jp/faq/12.html
照会サービス
Google trans: What is the outline of the ETC usage inquiry service?
This is a service that allows you to check the usage details online for up to 15 months from the date of use of the service for trips taken using an ETC card that you have registered in advance.

Other probably eijiro mistakes:
"referral of a patient"
患者の照会
患者の紹介	1359	96.7%
患者の照会	46	3.3%

I think this is just a bad gloss:
referral for follow-up care
フォローアップ治療のための照会

This is "inquiries (made by other parties) about your treatment", as in:
http://www.fhk.or.jp/kenkou_oyakudachi_contact.html
結果報告及びその他医療機関等から精密検査や治療のための照会に対しては、皆様の同意を得ている範囲内で対応いたします。

This whole novel is just to remove a term that I think causes more confusion than good.  If this already agrees with your intuition, feel free to not read any of the rest.

Up front, we have an entry already for 照会先 ("reference (e.g. for a job)") and 身元照会先, so those are handled.

sankoku's entire definition is 問い合わせ(ること）, which is slightly shorter than the daijs gloss. Seems like as a noun, this is 問い合わせ, and as a verb it is 問いあわせる。We don't have "refer" or "reference" on either of those.

This appears to only become "reference" in a very narrow sense, in things like 照会先. "inquiry-person" = "(job) reference".  I don't believe 照会 is used as [abbr] for 照会先 alone. 

〇〇に照会してください is *sometimes* glossed as "please refer to... (e.g. your local bank branch)", which is an elegant transformation.  But "please inquire at" also works, and you could make the exact same argument for glossing 問い合わせ as "referral" or "reference".
に問い合わせください	61833
に照会してください	1455

With regards to "referring" in the medical senses, it appears to me that there is occasional confusion between 照会 and 紹介, but that 紹介 is the correct term for referring a patient to another doctor. (a few random 照会 entries with overlapping English glosses seem to have added some confusion to eijiro). 

Like 照会先, credit lookup & reporting agencies sometimes get this in their name. "Credit reference agency" is a gloss I encountered for 信用照会機関.  Again, this is niche case(and we generally prefer "credit reporting agency" anyway )

照会させる = lit.  "made to inquire", could sometimes be glossed as "X was referred to ...".  Putting things in the causative form can do neat things to glosses, and we don't generally deal with this.

@@ -19,0 +20 @@
+<xref type="see" seq="1598590">問い合わせ</xref>
@@ -20,0 +22 @@
+<gloss>query</gloss>
@@ -22,2 +23,0 @@
-<gloss>query</gloss>
-<gloss>reference</gloss>

Meikyo vt and vi additions to n,vs entries
-*- via bulkupd.py -*-

@@ -18,0 +19 @@
+<pos>&vt;</pos>

@@ -19 +18,0 @@
-<pos>&adj-no;</pos>