Hello

Quote (Blizzard8088)

Will an Elec Element object regenerate HP on Solar Panels?

If it has an actual elemental affinity, than yes.
Just checked with a mod, Objects don't have actions that would trigger effects of terrain that trigger when someone takes an action on them. So no, I'm pretty sure they wouldn't be able to heal off of Solar panels, but feel free to PM an official or someone to double check.