the dipped and main beam do not form part of the blown bulb warning system guys, so for the blown headlight you're not going to see anything.
You could, if you felt that way inclined, get your multimeter out. Test the multiplug to the headlight and see which pins go live as the dipped/main beam come up. You're going to need to compare that then to the other headlight.
if the pins react the same then you've got a wiring fault in your headlight. If the pins do not come up the same then you've got a break in your wiring loom that feeds the headlight.
worst comes to worst I do have a suggestion, but I don't think it will be brilliantly received and isn't the greatest but would work.
For anyone that has ever fitted HID headlights, you're always recommended to fit these on an additional wiring harness, you could do the same here, just with a normal filament lamp.
For HID wiring harness you connect a relay to the bulb connector on the beam you wish to HID. This way when you turn on the lights it just activates the relay. You wire in a positive feed direct from the battery to the relay so the relay switches this direct live feed and when on fires the HIDs, or in your case a bulb. This is supposed to be done for HIDs as when they ignite particularly they need massive current which could overload factory wiring looms, so you fit a bigger stronger one in to be safe. don't forget to fit a fuse just after the battery if you do.
Again. not the greatest solution in the world but would work and if your wiring loom has a fault possibly the only option if you can't find what has broken.
1999 156 1.8TS Sport Pack 3
2001 166 3.0 V6 24V Super
2003 156 GTA 3.2 V6 24V
2005 156 1.9 JTDM-Jet Sport
2008 159 1.9 JTDM Lusso
1997 GTV 2.0TS Lusso
2001 147 1.6TS Lusso