I’m constantly getting the readings mixed up for jukugo containing these kanji. The nmemonics are helpful, but I tend to forget many for vocab items.
Is there a predictable pattern for how they’re read? I’ve been going off of ‘feeling’ up until now (whichever sounds the most natural), but something more concrete to go off of would be nice. It’s a bit lame getting the same vocab items sent back to apprentice because I used げつ instead of がつ or にち instead of じつ etc
There are no fixed rules to my knowledge what is used when (and if there are, they are probably a bigger struggle to learn, than any other way), but you will get the pattern naturally given time and will be able to pretty accurately predict, which is used when. But I’m not really into putting rules to everything in languages and can’t be bothered to brute force remember them, so someone else might be able to help you better.
Like with so many things in languages: keep consuming content, your brain will figure it out in time. If you don’t yet, there are more important things to learn first.
If the items itself are annoying you, you can either install the tampermonkey script to redo the items until you get them right. There really is not much damage done if you just be done with them for now, you will see them everywhere anyhow.
Or you do what SRS is supposed to do and try to do them over and over until you burn them into your memory. Bruteforcing is an option, can’t really recommend it though, not worth your time.
These come up a lot on the forums, so searching for what people have said previously might turn up some helpful tips.
For 月, it’s がつ when referring to a specific month, e.g. 二月, 十月, 何月 (何 being the placeholder for a number.) Otherwise it’s げつ. The only time it takes つき is when it’s referring to the moon (but this doesn’t mean that all moon terms take つき)
So in general:
Specific month: がつ
Moon related: つき or げつ
Anything else: げつ
Thanks for the reply! I was using the redo script for a little while, but I would catch myself correcting answers if I was close, which kinda felt like I was working around the SRS system lol. An argument could definitely be made on whether it’s more efficient to learn ‘why’ these things are the way they are vs just learning the material. But I am still curious 
This is super helpful!! Thank you * I didn’t know that つき was specific to context of the moon either
There are some つき words that don’t refer to the moon.
An incomplete list:
毎月 (まいつき) - every month
月々 (つきづき) - monthly / month after month
月一 (つきいち) - once a month
ひと月 (ひとつき) - one month (alternatively written 一月, but more often ひと月 due to reading confusion)
Sometimes the things are the way they are because of rather complex reasons. I’m sure there is a lot of culture, history and all kinds of other reasons, why the readings are the way they are in this case. It could definitely be an interesting read just for the usual curiosity, but I highly doubt that it will help a lot with language learning itself.
I’m a perfectionist in most cases myself, but needed to adjust at some point when it comes to languages. There is far too much to learn to take it all in consciously, just try to imagine how much syntax, semantics, vocab, history, culture, etc. you need to naturally aquire and be able to use to get “fluent” in a new language. From a logical standpoint it must seem impossible and yet people did it for thousands of years. 
Sorry, this has nothing to do with this discussion, I just like to talk about such things
One minor pattern: 日 is generally にち when it refers to Japan, like in 来日 or 日米.