Okay, you'll need to trace the wiring.
The reference is on p78 and 79 (PDF page 80 and 81) of TP32352/1 - a copy of which should be found in Oz Volvo's illustrious technical library.
The circuit runs from -
Black wires grounded at seat belt blockRed wire from seat belt block, to a connector, then 2 brown wires to cold side of warning lampsTwo yellow wires from the hot side of the warning lamps, to terminal [49a] of the indicator relay.
At a guess, the ground connection may have been removed from the seat belt block. Grounding the cold (ground) side of the warning lights makes them flash - they get their +12V from terminal [49a] of the indicator relay. The driver's seat cushion doesn't have a switch on it; but the front passenger's seat does (a normally-open switch) and it must be closed (like, when a passenger sits on it) in order to ground the connection to the warning lights via the seat belt block.
If there's no ground to the warning lights, they don't flash. Removing the ground connection is normally done by plugging the seat belt into the seat belt block, which disconnects the normally-closed switch within it that grounds the warning lights.
tl;dr? See the diagram; then it will all make sense.
Happy hunting.