I was quite comfortable with Robin's 2017 version and I don't think the proposed changes improve it. I'll add your extra gloss. I also think the note is not very helpful.

@@ -14,3 +14,3 @@
-<s_inf>esp. あやかりたい. e.g. 幸せに〜, 彼に〜</s_inf>
-<gloss>to share (someone's good luck)</gloss>
-<gloss>to enjoy the same benefits (as someone or something)</gloss>
+<gloss>to share (someone's) good luck</gloss>
+<gloss>to follow (someone's) example</gloss>
+<gloss>to enjoy the same benefits (of someone or something)</gloss>
@@ -18 +17,0 @@
-<gloss>to emulate (someone one admires)</gloss>

あやかりたい	63395
にあやかりたい	17707
あやかる	11682

Reverso examples (note the explicit objects with に、 it does not generally float on its own):
彼女の幸運にあやかりたい
おれはきみの性質にあやかりたいと思うよ
この自信に私は打たれて、坂田にあやかりたいと思ったのだ (have his self confidence, be like him)
その徳にあやかりたいと思って訪れると
おれのこの勇気にあやかりたいのだろうか。 
さうとすればあなたは一財産つくるでせうし我輩もそれにあやかるわけですからな。 (google trans それにあやかる: "I will follow suit")

だから英語は面白い: 会話上手はユーモアから
https://books.google.co.jp/books?id=J_h1BgAAQBAJ&pg=PT36&lpg=PT36&dq="emulate"+"あやかりたい"&source=bl&ots=oMngAbUWfp&sig=ACfU3U15HrE6smzSRcBBgW5Icl6G75PcNQ&hl=en&sa=X&ved=2ahUKEwjd-OT5peD9AhUW_WEKHb0ID1oQ6AF6BAgDEAM#v=onepage&q="emulate" "あやかりたい"&f=false

「あやかりたい」をどう訳す
“I would like to emulate him….” まねる, 模倣する、という感じの言葉で、copy とかimitateよりずっと感じの良い意味です。

https://eow.alc.co.jp/search?q=あやかる&ref=sa
capitalize on the popularity of

Among other things, moved the parenthesis.  

肖る seems to be about emulation - "resembling" some other situation, in the usual meaning of the kanji (肖像 = picture which resembles the subject). 

daijs says the thing is "usually positive".  But, to share in someone's happiness is not "肖る", it's "幸せに肖る" (so far as I can see).

We don't usually want to emulate negative things, or share in negative situations, so this expression usually appears with a positive connotation.

I saw the eow.alc.co.jp link from 2011, and Robin's example sentence "サッカーブームに".  eow.alc.co.jp  may have added the "to capitalize on" gloss since 2011, and it seems to be a more natural fit for this usage. (obviously the underlying concept, sharing in the benefit, remains... this seems like a little bit of an extension).

"ブームにあやかり" is an extremely common google news hit. 
https://prtimes.jp/main/html/rd/p/000000314.000018574.html
コロナ禍で広まったキャンプブームにあやかり、佐賀県民ならだれもが一度は訪れるであろう場所、「吉野ヶ里歴史公園」でのキャンプウェディングを企画しました。

@@ -14,3 +14,5 @@
-<gloss>to share (someone's) good luck</gloss>
-<gloss>to follow (someone's) example</gloss>
-<gloss>to enjoy the same benefits (of someone or something)</gloss>
+<s_inf>esp. あやかりたい. e.g. 幸せに〜, 彼に〜</s_inf>
+<gloss>to share (someone's good luck)</gloss>
+<gloss>to enjoy the same benefits (as someone or something)</gloss>
+<gloss>to capitalize (on the popularity of something)</gloss>
+<gloss>to emulate (someone one admires)</gloss>

gg5: "サッカーブームにあやかろうとこの町の菓子屋がサッカーボールの形のケーキを売り出した.　Intending to benefit from the soccer boom, confectioneries in this town started selling cakes made in the shape of soccer balls."

@@ -14 +14 @@
-<gloss>to share good luck</gloss>
+<gloss>to share (someone's) good luck</gloss>
@@ -15,0 +16 @@
+<gloss>to enjoy the same benefits (of someone or something)</gloss>