The motor sequencer had been replaced with a solid state unit in 1970. They do fail (after 45 plus years - go figure).

Here's a couple of trouble shooting sites for this exact issue:

Troubleshooting 1969-1973 Cougar, T-Bird, & Shelby Sequential Turn Signals

http://www.thuntek.net/cougars_unlim...wDiagnosis.pdf