Wot's the 1994 Volvo 940 owner manual say? You still have an owner manual? I think there's some mention as to interior lighting in the Volvo automobile owner manual.

Else, without certainly whether you have the fading dome light like later luxury 900, and seemingly most FWD/AWD Volvo, please see:

http://www.volvowiringdiagrams.com/?dir=volvo/960%20Wiring%20Diagrams

You can review the wiring diagram for your model and year Volvo 960 to see if the fading dome light option is in the car and the components. If yes, though I'm unsure, something like a relay, that is a relay, would control this function, probably on the relay board behind the ashtray at the bottom of the center dash console.

A visit to a junkyard with later 960s can help you before you mean to take apart your own Volvo to repair this fading dome light function.

A search on brickboard.com or, using google, search www.brickboard.com using search terms to find your problem. In your web search query, to target a domain use the search expression:
site:www.brickboard.com

You may find other article on this same problem with later 960.

If the rubber shrouds have come off, or are stiff and ripped, from the hinge-side door pillar mounted dome light switches, these switches can become corroded, and an intermittent continuity signal to a fading dome light relay, certainly older designs, can be interrupted in the fade out function with sporadic continuity. You can get corrosion where the wire harness wires terminate on the hinge-side door pillar switches.

Hope that helps.

Other with actual 960/940s may chime in with direct experience with this fading dome light issue in 960.

Thanks,

Duffed.