Not true-ABS light does not come on when ABS is activated-TC light flashes when TC is activated, same with ESP 
Are you saying the MIG doesn't alert the driver if/when the ABS takes over?
If so, I'm going to double check that this week by taking my mates MIG out and intentionally bringing about a situation that would cause lock up on a car not fitted with ABS.
Not had the Omega long-but he's on about a Galant front wheel drive.
In 87 cars, never had one where ABS light notifies you when it kicks in, but all traction control equipped cars have flashed the TC/MSR whatever daft acronym warning light when activated, same with ESP sytems.
Some ABS cars have driven me nuts with over-sensitive ABS-the Berlingo was one-it kicked in way too easily if only one wheel lost grip and worked on all four wheels, sending you careering onwards if only one wheel lost grip. Crazy!
I noticed it most on a Suzuki Swift 4Grip which is was due to trade in, so replaced a punctured tyre with a cheapo tyre and left the other 3 decent quality tyres on. Every time you braked, the cheapo would lose grip and cut in the ABS as the sensors noted a difference in wheel speeds.
Fairly new to Omega, so not an expert except for the useful info learnt off here-so may be different on Omegas-but never known an ABS car to light the symbol when activated.
It is normal for TCS and ESP to light when activated however.
I think the issue with the Galant is the tyres-wrong pressure, cheap quality, part worn, cold weather, hard braking. Add poor tracking, poor road surface, dodgy brakes, worn suspension into the mix it just gets worse.
If it was mine, I would start with the tyre pressures, then check the tyres over first, modify driving style, then look for a more complex ABS answer after
