For my 92, a Tech-1 is needed with the brake system plug-in module. That allows the Tech-1 to power up and run the ABS pump. But everytime you start the car and move forward thru about 4MPH, the ABS pump does a self-test and some fluid moves thru the pump.
You could do a brake system flush and cycle the ABS by starting the car and moving forward until you hear the ABS pump run and then stop. Then shut the car off and repeat. I don't think the ABS pump contains a lot of fluid so it shouldn't take a lot of repeats. Probably just driving the car everyday for a week should get the new fluid into the ABS. The 87 service manual mentions an "ABS Diagnostic Tester" and it may be that the early C4's had to have separate diagnostic devices for the various systems. The Kent-Moore number is "J35890 ABS Tester"
I had gone to the dealer a couple years ago to have a fluid flush done and the service manager talked to the brake specialist and he said that that procedure wasn't really necessary unless there was a problem with the ABS pump that required its removal.