A friend's XM had no dipped beam and as I have dug out the wiring diagram, I might as well post here.

Normal operation is that the high beam will always flash and can be turned on without the ignition. Dipped beam only operates with the ignition switched on. It bleats if the stalk switch is on and the car is not running.

Here is a diagram for early LHD cars, but it appears to carry through mostly unchanged.

XM Headlights-xm_headlight_wiring_lhd_earlys.jpg

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The dipped beam is supplied with battery voltage via relay 825, which is behind the RH headlamp. It looks to plug into a green socket.

Ignition switch 300 feeds (in ign on posn) 12V to the lighting stalk 211 and then (if switched on) feeds 12V to relay 825 at pins marked 5V4 and 5V1. That means pins 1 and 4 of the green 5 way socket for the relay.
Low beams are 486 and 487. High beams are 502 and 503. Since high beam worked, the body earths m1 and m2 would be OK. Following the connections at relay 825, it should be easy enough to test the circuit with a multimeter.

Most relays have their circuit and pin numbering marked on the case these days. Don't mix up relays as ratings vary and some have an internal diode, such as the start relay behind the LHS headlamp.