I still have my childhood IIGS. It sat in my folks’ poorly insulated attic for two decades before I rescued it, and it booted up on the first try! They don’t make ‘em like they used to.
Their power supplies have RIFA brand capacitors in the power supply. Their cases are 100% guaranteed to be cracked from moisture ingress at this age. They will fail catastrophically when you plug it in at some point. If you want to keep it running, you need to replace the supply or recap it (Just the X & Y RIFAs).
Replace the 3.7v lithium backup battery for the RTC before it blows up and spews acid all over your board! ROM01 versions have it soldered in, ROM03 is in a battery holder. Replacements for both are readily available.
NP - BTW just checked my Mouser order history, if you want to add a removable battery holder to a ROM01 board you need a battery holder #108 and retainer #108C. The same Keystone brand holder is used on the 03 boards.
As someone else said, google Apple RIFA caps and replace them. They are 100% going to fail on you and damage the machine. It's the first thing you do when purchasing an old Apple.