Your "gen" light can be on for a number of reasons.
firstly you will have to tell us what make and model car you are referring to, some cars have different wiring so having the gen light could mean any number of things. eg: a blown fuse. Be a little more specific. Also look to see if the gen light is on when you turn the key on but not with the engine going.
good luck
The gen light stays on when the charging system malfunctions.
If your GEN light is on then the generator votage has reduced down to an extreme low rate or it has died completely, as in, it isn't putting out voltage to recharge the battery.
Gen:1:3: And God said, Let there be light: and there was light.
The GEN light is supposed to light up when the car is started as an indication that the light is functional. If it remains on after the car is started, however, your generator (alternator) is either malfunctioning or not working.
To replace the light, it all depends on the year of the Accord. I have a 5th gen(94-97), and I know how to replace the 4th gen(90-93)
It is an indicator that the alternator is not charging.
It means there's a problem with your charging system.
The alternator/generator is not charging.
The alternator is under or over charging.
That would be short for "generator" light. If that light is on while the engine is running, the charging system is not working and you are running off of battery power only.
I have a 76' Malibu and almost the whole time I have had it the gen light is on except when I just put a new alternator in it. Then the light would go out for a while, but always came back on after a while. What I found out was there is a Diode that goes bad in the alternator and causes the light to come on. Soon you have to get a new alternator.
The alternator has a serious failure.