Yes, like Spook says, presuming you have the ground and contacts all cleaned up and snug then it's likely the bulb sensor relay. If you're not familiar, it's the round red relay, back left corner of relay tray. For access, remove ash tray and fuse panel cover, remove storage box (two screws behind bezel surrounding the lighter socket), lift relay tray at front and pull forward a bit to get enough height clearance at the back. Often easiest to pull surrounding relays to get a better grip.

They're not overly cheap or easy to come by locally so try to borrow one for testing purposes or maybe get a used from a yard hoping it's okay. All 240s/740s/940s from 1986-on use the same bulb sensor.

Hella made the original relays for Volvo, but Kaehler (KAE) now supplies them using a different internal design with electronics instead of counter-wound coils and reed switches. I've recently had problems with two new KAEs being way too sensitive to voltage or current fluctuations (tested in two cars). They may have been from the same bad batch.

For those handy with a fine tipped soldering iron, the original bulb sensor relays can often be repaired by re-flowing the solder at the major connections on the two tiered boards inside. Some are a bit difficult to access. You usually only need to worry about reflowing the main connections for the pins, jumper stakes and sensor coils for the problem circuit. In your case you can trace the brake light circuitry between pins 54S (input from the brake switch), 54L (left rear), 54R (right rear), and S (3rd brake light). The headlight circuit is the next most troublesome, so while you're in there you might as well trace and re-do the circuit between pins 56b, 56bL and 56bR. You can usually leave the solder joints on the sensing circuit alone, like the tiny little reed switches, resistors, caps and transistors. Do not be tempted like me to bend and straighten out the delicate reed switches going through the middle of the sensing coils as the ceramic coating becomes brittle with age and heat so can easily crack and expose the contacts (resulted in a later internal short that gave me a bit of grief).

If you don't have a spare for testing or don't want to attempt re-soldering then before condemning your bulb sensor it might be worth doing some simple further testing to see if the symptoms are more than what you've indicated to us.

a) With the park lights off (meaning key off as you have permanent DRL), does your right brake now also light at the rear when you depress the pedal? If it does then that may point the finger away from the bulb sensor. Oh, and just in case you haven't figured it out for yourself, for single person testing purposes it's handy to use a stick wedged between the seat and the brake pedal to trip the brake switch.

b) Disconnect the right brake light yellow wire off the back of the light assembly (tape it and keep it away from chassis metal). With the park lights on as before, when you depress the brake pedal does the right rear park light still go out (in addition to the right brake light not being on)? If so, that may also point the finger away from the bulb sensor.

c) Using a half decent ohmmeter (at like an RX1000 setting), with everything off and disconnecting all other wires at the right rear assembly except leaving the black ground wire still on its tab, when you measure between the metal ground strip on the light assembly and chassis ground, do you get near zero resistance? There's not a lot of clean bare metal back there, leastwise not in wagons (the small screws in the tailgate opening aluminum floor trim strip are not ideal but will do as a start if you can get a zero reading between two screws to know they're okay to use). Move your taillight test point further up the ground strip to the corresponding contact on the back of the brake bulb holder (basically as close as possible to the bulb base). If you're not getting virtually zero ohms to a good chassis ground at both test points then you need to go back and clean up all ground contacts and wiring connections. Pay special attention to that taillight chassis ground stud, which on wagons lives inconveniently just inside and behind the side panel -remove the taillight assembly for improved access. At the very least, loosen the nut there, spray contact cleaner and rotate the terminals back and forth a bit as you re-tighten the nut to see if that at least temporarily improves things. It's best to open that ground right up, polish all contact surfaces and use something like De-Oxit or at least dielectric grease to protect from corrosion.

And finally, the continuity behaviour you witnessed through the double filament brake/tail light bulb is correct. Think of how these bulbs are constructed as a "T" with one filament in each upper arm of the "T" and the bottom of the "T" connecting to the metal bulb base. Looking across between the top two contact points is like looking through one big long filament. Resistance will of course measure differently between any two points depending on the amount of filament the test current has to pass through, but for the sake of declaring a yes/no continuity, current can still pass.
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Dave -still with 940's, prev 740/240/140/120 You'd think I'd have learned by now