Most of the proper function bands I've worked in have pads of several hundred numbers. It's not possible to learn all of them, so being a fair/good reader is of great use. This way, new numbers can be available on a gig to be played at sight as and when needed. This also saves spending (wasting?) a lot of expensive rehearsal time.
Being able to read well means you can play in various styles by doing what the charts say. Having a guitar/s that give a variety of sounds is also useful - pedals, boards, a reliable amp go without saying.
Be prepared for anything: a complete change from what subset you may have expected next. Someone (a guest) asking if they can sing xyz in Eb. Your music and stand being knocked over by someone merrier than yourself - and you do carry on...). Having to suddenly take a lead break when the horn player's mic goes down. Being aware that the bandleader decides to stop a number in mid flow. Being asked to busk a number that you've maybe heard before, in an unfamiliar key.
Looking and acting in a professional and respectable manner is also expected. Don't take problems on yourself at a gig - leave that to the bandleader. Timekeeping (both in being there set up and staying in tempo) are good points. Arriving late for a gig was the last time you'd play with several bands!
Having said all that, your sort of function band may not be anything like the kind I play in...