I do not know exactly how Volvo blinkers work, but the blinkers on most cars work on current.

The current flowing through the blinker heats up a bi-metallic strip. The more current, the faster it heats up.

Usually if the blinker runs slow, there is a lower than normal current flow, that is, one of the bulbs is not working.

If the blinker works rapidly, the current is high, caused by a short circuit or extra bulbs on line.

I would check the added wiring on the bad side. If you do not want to pull the wiring apart, remove or disconnect the extra bulbs.

Check the grounds on the bad side, if the ground is bad, you could be feeding the driving lights through the side marker light.

It is possible that you are feeding current to all the bulbs that you mentioned, but they are not lighting up bright enough to see.

Did this problem show up after you added the side markers?
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2 8s & 2 7s 600,000 miles total

My 94 940 did the exact same thing a few months ago. It needed to have
a socket replaced. It's the actual metal socket that holds the bulb.
Can be gotten at a Volvo parts store, easy to replace. HT

90 244DL 133K
94 944T 92K

are you 100% sure the bulbs themselves were actually lighting up when this occured?

usually this is a sign of one (or both) bad bulb(s)
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http://www.fidalgo.net/~brook4/oilslubesfilters.html

Have you checked that both front and rear left turn indicators are working when this happens? This is normally an indication of one bulb not working or drawing insufficient current through a bad connection.
It could be a bad connection anywhere between the indicator switch contacts and the actual bulbs,most likely a bad bulb or bad bulb contact though.
Colin.