Probably enough now. People can read the comments.

I don't think "express a desire" is ideal - I would read it as somebody explicitly saying they want something, when that's not what this 
means - and "to display want" sounds a little unnatural to me. "to indicate" also sounds very intentional and while it can be, it 
certainly doesn't have to be. It also sounds like the "wish" is being pointed out quite clearly when this is more about 

私 being the subject is rare but when it is, the context is about somebody else reacting  e.g. by noticing the speaker's feelings and 
buying something for them. e.g. google results for "私が欲しがって" (all from the first page): 
"空港で私が欲しがってたらきゃんちが買ってくれたお魚シート♪( ´θ｀)ノ"
" “私が欲しがってた バスの降車ボタン 娘が見つけて ガチャってきてくれたよ"
"友達以上恋人未満の彼から、私が欲しがってたアロマセットをプレゼントしてもらいました。"
"夫「ガレージにきて」私「うん」→私が欲しがってた新品のバイクがドーンと置いてあった！"

daijr: ほしいと思う。ほしそうなようすをする。
I think "appear to" (ようす sense 2: "look; appearance") and "seem to" work the best fit here.

@@ -20,2 +20,3 @@
-<gloss>to express a desire</gloss>
-<gloss>to display want</gloss>
+<gloss>to appear to want to have (something)</gloss>
+<gloss>to obviously want</gloss>
+<gloss>to seem to want</gloss>

ルミナス:
父は僕がいつも欲しがっていた自転車を買ってくれた My father bought me the bicycle (which) I had wanted for a long time.
その子はアイスクリームを泣いて欲しがった The child cried for ice cream.
GG5 (-がる)
(1) 〔…という感情･感覚を表す〕
(2) 〔…したいという気持ちを表す〕

I was going to comment that it seems only to be used in the third person (as in all 11 sentences), but then I saw that ルミナス example which is first person.
I think GG5's explanation is good -  the ...を表す is important, It's more about expressing and stating rather than appearing.
I'll suggest some tweaks.

@@ -20,3 +20,3 @@
-<gloss>to appear to desire</gloss>
-<gloss>to seemingly want</gloss>
-<gloss>to apparently wish for</gloss>
+<gloss>to express a desire</gloss>
+<gloss>to display want</gloss>
+<gloss>to indicate a wish for</gloss>

meikyo
が・る〘接尾〙
…という気持ちや様子を外に見せる意を表す。「悲し─・欲し─・恥ずかし─」「寒む─・痛た─・怖わ─」「新し─・珍し─」「いや─・不思議─」「眠た─・煙た─」「会いた─・知りた─・話した
─」「粋─・通─」「強─・得意─（＝ぶる）」 感情や感覚が外部に現れた様子をいう。「悲しがって（＝悲しそうにして）いる姿が哀れだ」

The point I was making is that it won't be obvious from the original glosses that this is a verb you only use to describe what others appear to want. You 
wouldn't say X私はこれほしがっているよね to say "I want this", and I think this needs to be made clear in all -がる entries.

My problem with this suggestion is that none of the 3 JEs I use has any mention of appear/seemingly, and none of the 11 Tanaka sentences does either. The closest I can see is a また at the end of Koj's explanation. The original glosses are pretty close to the ones in the references. I suspect it's used just as a verbification of 欲しい.