The primary cause for jerking on a 99 Mercury Cougar is the engine not getting enough fuel. This can be a sign of a clogged fuel filter, bad fuel pump, or clogged fuel injectors.
it is in the manual says when this happens it is 02 sensor and if it is flashing you have a miss in your engine which can cause damage.
The most likely cause is a dirty fuel filter that starves the engine.
you dont need to cause it has a factory tachometer
probably the fuel pump?
I had the same problem in my 1999 Mercury Cougar, I replaced the flasher located in the blinker assembly. It was very simple to do. Flasher cost about $10
my son bought a 1996 cougar that felt like the transmition was slipping and we had the transmission flushed and it fixed it.
Possibly the new thermostat is bad...........don't laugh it can happen. I'm not sure if you could have installed it upside down. Sometimes that is possible but I am not familiar with your specific engine application.
the ignition timing set wronge. BAd accelerator pump in the carburetor
The gears in the speedometer are stripped. If the odometer is working then you have input.
check the recalls for the 99 mercury cougar!! it includes a recall on the throttle cable...
* No power steering fluid in reservoir * The power steering pump is not operating