I am not familiar with the North American light setup on these old Volvos, but I would imagine that they are not that different from European units and that inside the engine bay things look like this (1992 model, in this case it's the driver's side):

Given the two wires on the grey connector, I'd say that one is for the running light and one for the indicator. Return path is through the black wire fixed onto the bodywork just outside of view.
Here's what I interpret and deduce from you description:
-Since the running light works, that means that the return path is ok, as it will be shared by both bulbs.
-The direction indicator relay works because all other indicators work.
-The stalk on the steering column works as the rear indicator works.
Here's what I would do:
With known good bulbs in the unit, unplug the grey connector and measure continuity on the black half between one pin and bodywork repeating the measurement between the other pin and bodywork making sure both probes have a solid contact to pins and a bare metal part of the body.
If continuity fails on one of them, that's your indicator and the problem lies in the unit. If continuity is OK, however, then the problem lies upstream.
My guess is that the problem will likely be in the unit, so lets focus on that now.
The indicator/running light unit slides and locks onto the headlight housing. So you will have to unplug all connectors to the unit, unscrew the black wire from the bodywork, remove the grille, unscrew the hex nuts from the studs of the headlight housing and lift the assembly away from the front being careful not to snag the connectors on something and have it pull out of your hand and drop glass first on the pavement (been there, done that, cash changed hands the same day).
You can then lift the lock tabs and slide the unit off the headlight housing for easier access.
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