I think I don't understand this sentence/maybe why the conditional form doesn't have something directly after it and before the と in this sentence

Question

Context: A new school teacher doing her first ever parent teacher conferences hasn't been able to get in contact with the mother of one of her students. She has tried to contact the mother for weeks, and leaving another voicemail for the mother the teacher says:

"お時間のある時にご連絡いただければと思います".

I think I understand that the meaning of this is maybe something along the lines of "When/if you have the time, I would be glad/happy to receive your contact",or something, but I don't understand how the いただければと思います has the meaning that it does/contributes to the meaning of the sentence in the way that it does?

More specifically, when I first saw this, I thought it might seem more understandable, to me, if there was an いい or an 嬉しいになります or something after the いただければ. I just don't think that I've ever really seen the conditional and then the quoting particle right after...though I also see that maybe it could like make it more polite or something somehow maybe to not say anything after the いただければ?

Thank you!

Answer 1

I thought it might seem more understandable, to me, if there was an いい or an 嬉しいになります or something after the いただければ.

This is it. As you suspected, something like "I'm glad" or "I appreciate" has been omitted after いただければ. This is just another common pattern that indirectly expresses your hope/request. It works alone, without と思います, for example:

• 明日も来ていただければ幸いです。
  明日も来ていただければ。
  I appreciate if you come again tomorrow.
  I hope you come again tomorrow.

(幸い is a way of saying "I'm glad" suitable in a formal situation.)