My solar backup system is wired to run all my PC hardware, Fios box, combo wifi-modem unit.
It uses a MSW inverter and I've tested it out on my loads. Seems to work okay.
But, I have not been using it during times of bad weather or snow melting.
Since my primary app for back-up is to run my sump pumps.
Using Solar PV to take over a (12V 2A) 24w 24-7 load would likely cost you more than it's worth.
You would need to be able to quickly recharge the battery and feed the load at the same time.
Maybe you could build it bare-bones and could manually switch back to the grid when the battery got low.?.
A few cloudy days in a row.
Maybe a 100w panel and a charge controller that had a load controller built in.
The load output would shut down when the battery got too low. Like this one. Saves the life of you battery..
Morningstar SunSaver Charge Controller, 10A, 12 VDC