Hi,

Some of those relay might be for electric Windows.

The blue wire is shown connected into the whole works. I saw this in the follow link to diagrams.

http://www.volvowiringdiagrams.com/volvo/240%20Wiring%20Diagrams/Volvo%20240%201989.pdf

This is for a 1989 for generalities being I have not seen what year car you are working on.
These few pages cover a lot of those relays found in many year cars.
Glance over them all to get a sense

Around pages 17 or 18 are diagrams showing headlights and taillights.
The bulb out sensor is intertwined with in thes components of the dipper relay outside. Look over the wiring following the wire codes in the diagram.
You want to follow power supply to these things not working. Some people can work back towards where the power supply shows up, like your 4volts!
All of these outside components have connectors that can get damaged by weather or humans.
Relays get wet internally, out there, of which, strange things go poof!

These are monitored by the bulb failure sensor relay. I m not sure what causes these to fail but I suspect bad wiring helps start the wires inside to fail or they could be just fragile and die of old age.

Either way 4 volts mean not good continuity for electricity to travel.
Using the diagram like a road map to follow colors of power and grounds for returning power. This is to and from or even through things to see where it stops or should be going to next.

Expect full battery voltage, with a meter along the routes. Some people like test lights as long as you know which way you are expecting a circuit. 4 volts would be a very dim light or none.
So I'm glad you know your volts!

I need to ask what year is your car?
Do you have a light in the instrument cluster that says you have a bulb out?

If the sensor is working and the instrument light should be lit. Trouble is it does not tell you where even if it's working fine. It will tell you if it comes on when a signal is used or a brake light!
It will say all others are possibly bad when the whole lighting system is used. The license plate lights, I think, are excluded.

When you first turn the key a testing of all dash indicators are done.
Are they all working?

Now we need to know if any lamps are burned out by testing them individually. This is to where we know it's the wiring to them that's failed. Have you done that? Most people do out of recourse as an elimination technique.

Now we have discussed corrosion in key places and need to move to breaks in connections which include switches or that sensing relay.
Switches usually control entire bunches of circuits at once or as an individual one.

So far, you have not found damage to any relays or switches from heat. You have gotten yourself acquainted on how to dig into the car by now too! (:-)

Have you found that round "can" under the dash? Can you look down or feel from above through the instrument cluster window and find that can?
Probably better to work from where it will hang down.

We need to check for voltages on those wires on it to see if any wires that are coming in or out are working.
The reason I suspect a problem is because the bulb failure sensor has lost contact with those two circuits. The headlight and the taillight on one side.
Listed in the diagram on that sensor is left or right sides of the headlights with the dipper relay.
Also the left or right of the taillights are depicted to one part of the relay.
Just seems to me a good place to test from! A joint where things meet, per say?

So try to work with the information and see what you find.
That is about all I can do from here.

Phil