My front overhead light will not come on when I open driver or pass door. The center light does come on. The front lights can be manually turned on when I push them. Should they light when door opens?

 

Sounds like this vehicle is new to you.
Easiest place to find that answer is in the owner's manual.
If you don't have a copy, you should be able to find it on the GM.com site. There is a section for nothing but owner's manuals.
Google it first it will save you a lot of time

 

The dome lights come on if switched to work. The map lamps come on if you push them. No where does it say in manual if map lamps can come on when doors are opened. Therefore, it seems map lamps are only manually switched.

 

Seems like adding a separate additional light might be cleaner, added in parallel to the dome light, provided you do not exceed the amp draw for the entire circuit and blow the fuse.

The wiring is rated for the maximum amps it can safely carry. That is one of the reasons that you should never replace a fuse with one of higher amperage.

​​​​​​Plus you then get to decide where the new light goes and how bright it is.

What year vehicle?

With the newer vehicles you need to be careful not to Make the BCM upset if is monitoring the behavior of the circuit. It wouldn't throw a check engine light, but it probably would throw body codes if it thought there was an issue, and it might shut down the circuit entirely. Don't know, just hypothesizing.

If they are being used to provide additional lighting while entering the vehicle, If you leave them turned on when you turn off the vehicle, restarting the vehicle should turn them back on. If you have a remote start, this I believe would address your need. If not, you'd have to wait until the key probably hits ACC after the driver gets in.

 

The map light on my equinox comes ON when door opens. And I can manually push them on. They only come on manually in the vue.