Warning lights are coming on but seem sensitive to bumpy roads so maybe a bad connection somewhere.  In detail

 

Battery light comes on and stays on when the engine is not running.  OK

Light goes out when engine started and idling.  OK

Light stays out when running during the daytime.  OK

Battery light and washer fluid lights come on at night when the headlights are on.  (But obviously there's no washer fluid sensor so light is spurious.)  Not OK.

 

Any suggestions where to start looking?

Try the battery terminals and alternator connections first, maybe battery earth terminal

is one slightly loose if problem starts on bumpy roads

31 minutes ago, AlanJD said:

Battery light and washer fluid lights come on at night when the headlights are on

How about when the HRW is on?

Have you also checked the battery is charged or not too weak? 

 

22 hours ago, KenONeill said:

How about when the HRW is on?

 

The HRW doesn't affect the warning lights.  (But a good suggestion.) 

 

I'm giving advice at a distance so the car isn't currently in my driveway.  I think the warning lights (headlights, battery) are close (adjacent?) on the display.  Is it feasible that there's some bad internal contact which allows the power to the headlight warning light to also reach other warning lights?

If there is a corroded circuit board etc then perhaps. The only way to know is to look, though. I would have thought a short would have worked both ways, though. If the headlights illuminate the battery light due to a cross, would not the battery light illuminate the headlight etc.

 

It might also be a wire chaffed somewhere along its route to the dashboard but unless you have interfered with things, unlikely. 

1 hour ago, AlanJD said:

 

The HRW doesn't affect the warning lights.  (But a good suggestion.) 

 

I'm giving advice at a distance so the car isn't currently in my driveway.  I think the warning lights (headlights, battery) are close (adjacent?) on the display.  Is it feasible that there's some bad internal contact which allows the power to the headlight warning light to also reach other warning lights?

 

That can be the next possibility, dry joint on dash pod or cabling not fully seated/plugged in.

I know this is an older topic but I feel relevant. 
our fabia mk2 1.6 tdi developed faint warning lights which were traction light and washer bottle warning. Also with ignition off when entering the car, the door open light also faintly illuminates the oil light and I think one other. 
Any way after lots of bad words and wiggling things, battery check etc. I found a similar fault online of an Audi a3. Their solution was a dehumidifier!! So I warmed the car up, in went the dehumidifier and hey !!! All faint lights gone. So turns out it was damp bleeding current. 
took maybe 2 hours for it to be fixed. 
I hope this helps anyone else with this or similar problems. 
all other things like this I found online never came back with their fix.