1) Facebook algorithms favor those pages that post more. So the more you post, the more likely people are to going to see any 1 post.
If you only post once in a while, as your guitarist suggests, then pretty much, no one will see it.
For my small business page, I make it a goal to post once a day.
2) Everything posted on the band site should be "shared" by each member on their personal page. FB algorithms will pick up on this as a page that is getting a lot of action. And people who see the bands post on your personal pages will count toward views. One one page I manage (not music related), we have 100 likes on the page, but we got over 700 reaches on a post from numerous people sharing the post. Yes, we got 7 times more reaches than we have actual likes. It is possible.
For my business page, I share most of my business posts on my personal page. The result is I have some 300 likes on my business page, but I get a reach of 200-300 people per post.
If you have 4 or 5 band members each sharing every post to the bands page, there is little reason you shouldn't have a wide spread reach.
The more you post, the more you share, the more FB will favor your page in their algorithms.
3) So you have 3 weeks between gigs. So, have someone take 21 pictures at your gig. Better yet, have them take 50 and select the 21 best. Post a photo a day. There, now you have 3 weeks of content. You'll see the number of likes and the reach go way up by posting daily.
4) This all said, don't get obsessed with how many views or have much of a reach you have on any given day. That's not the point. The point is to have consistent updating so that when someone new comes along and views your page, they see the page is happening and an exciting page to like. If you only post once every few weeks, people are going to think either you're no longer a band, or that you don't take your band very seriously, and probably aren't very interesting to go see.