Ok, I looked at the fuse box cover, and it has a picture with numbers of all the fuses and what they operate.
The cover agrees with this picture at this site;
Chevrolet Suburban (1997) - fuse box diagram - Auto Genius
Number 3 is for the courtesy lights,,
and the power mirrors.
I'll have to check the mirrors, they might be the culprit.
With ~4 amps of draw its got to be a connection that has fairly high resistance,, like a motor winding.
A direct short would just blow the fuse.
Those mirrors have been exposed to the constant rain here in Oregon for 23 years.
If water has got inside a motor/actuator, that might be the problem.
When the weather is better
, I'll check them out.
Another thing; how does the "timer" for the dome lights work?
Could the timer shut off the dome lights but still draw power?