I would be interested in learning how to wire up a transfer switch if you happen to have a good resource to link to. I also have an old UPS and was planning on just buying a new battery, but I already have an inverter and would rather have a larger battery if possible. The only auto transfer switch I found for sale was $50 on amazon and for a little more than that I could just put a new battery in the UPS and be done with it. But I am quite comfortable with DIY stuff so if that's an option I would much prefer that.
Sure, it's pretty straight forward actually. If you want something a bit more plug and play, you can get a transfer box like
this one. Basically, one plug goes into the wall, the other goes into your inverter, and there's a single output into which you plug your aquarium equipment. When the plug that goes into the wall loses power, the transfer switch fails over and starts pulling from the inverter. It automatically switches back when the power comes back on. For my system, I've attached a battery maintainer to my deep cycle battery. When the power comes back on, the charger comes on too, and automatically tops off and maintains any power that was used during the outage.
If you're comfortable with a bit more DIY, you can build a transfer switch even cheaper (around $10) using
a DPDT relay. If you're not familiar with how relays work, you may want to just get a ready-made switch like the one above. To summarize briefly, a relay switches power when its coil is energized. There is a common connection (COM), which you could think of as your output. Then, there is a NO (normally open) and NC (normally closed) connection. When there is no power going to the relay, NC is connected to COM. When the relay is energized, NO (normally open) is connected to COM. With the relay above, you would simply connect a female extension cord or outlet, which goes to your aquarium equipment, to COM. You would then connect your inverter's output to NC, because when there is no power and the relay is closed, you want to draw from your inverter. You would also connect your wall power to NO, because when there is power coming from the wall, you want to pull from the wall. You would also need to connect the relay's coil to the wall somehow to run the whole thing.
It's worth noting that you're playing with 120VAC if you choose to go the DIY route, which can easily kill you. If you don't have electrical experience or you haven't worked with relays before, I would strongly consider buying the ready-made transfer switch.