you could certainly try intermitent 30 minute aeration, I would think to do no more than a 2 hour break at first though. This is the company whose pumps I've used the most and they are absolute work horses that can take all the abuse I have been able to dish out
ecoplus air pump. For a 5 gallon batch the sun $20 version will work fine, the $33 one that is first on the google shopping link would last the rest of your life and could be passed on to your grandkids.
When you experiment with your air
mattress pump just trust your nose, as long as your tea stays smelling fresh and sweet then things are going well. If you start to get a sewage smell then it sat too long (although aeration might get rid of that smell).
and typing this I am reminded that the very first attempt I ever made at compost tea we were living with absolutely zero electricity, it was spring and very chilly at night/in the morning, we heated up some big pots of
water over the fire to add to our trash can full of cold spring water and would just take turns stirring it whenever there was some down time. It didn't get gross, though I don't know how effective it was. So you can't do any worse than that!