I have a string of Christmas lights permanently installed over the sofa...DW like the ambient light...and they are line voltage so that helps somewhat...but they are switched and not in your face.....so not a perfect solution.
More to the point of what you want.....I installed a remote switch in my dash to start and stop teh genny, along with an indicator light.
I can't believe I don't have a picture of the install. Basically, I tapped into the wiring at the plug shown in this photo.
I ordered this light https://www.ebay.com/itm/PLB6-R-ATI-6mm-1-4-Red-12V-LED-Metal-Indicator-Pilot-Dash-Light-Black-Body-/322447106827?hash=item4b1358630b
and this switch https://www.ebay.com/itm/Cole-Hersee-58027-04-SPDT-Momentary-On-Off-Momentary-On-3-Blade-Rocker-Switch-/253252383986?hash=item3af704b4f2
some 4 conductor 18 ga wire, and some connectors
You could easily just do the light without the switch if that's all you need.
Alternatively, if you already have a dash switch, you could probably find a lit replacement for it.
The generator has the wiring for the light (and remote switch)...you just have to tap into the circuit.
It would take just a little digging into the schematic to find it..... don't have mine handy at the moment, but yours might be different anyway. Get your model number and google for the schematics. If you need help, post the model of your genny and I (or someone else here) I'm sure would be happy to help.
One comment about my light.... it's bright at night. I on purpose installed it down low on the kick panel just above my knee, and blocked by the gear shift lever while I'm driving. Durring the day I can see it's reflected light, or just lean a bit to check it. Worked out very well I think.