So I've been chasing this gremlin with the idle dropping out.
So far I have replaced: inline fuel pump, filter and check valve, plugs, distributor cap and roter, spark plug wires, fuel injectors, fuel pump relay, and the injector timing relay, we find that when coasting ( like while in traffic) at 1000 RPMs and applying the break quickly, the idle drops to 500 then comes back up to 800 and stays there. Every time the break is applied hard. If the break is gently applied it doesnt do it.

Coasting at 1000 PRMs. do a quick stop. Rpms momentarily drop to 500 then immediately return to up 800. When at a stop light, it idles smoothly at 800.

any ideas out there?

Your issue is likely vacuum related. Where...not 100% sure from a distance but at that age it could be every vac line and check valve or the booster itself. Or, since it is a turbo, does yours have the electric vac pump?

Start with the bigger line...cap the booster port and try again.

a little more info: 2 weeks ago the idle was dropping out or a "mis fire" was occurring while stopped at a signal or stop sign. Then the car was a "no start".
Investigations showed I had spark. and I had gas up to the injectors. That is why I replaced the 2nd relay, the injector timing relay. With the new relay the car started right up. now this weird thing occurs: when coasting, foot off the gas, at 1000 RPMs and you hit the breaks, idle drops to 500 and returns to 800 .

Maybe I need to clarify. Idle is controlled almost exclusively by the IAC...little thing that meters air in going into the intake after the throttle plate using a spinning disc (oversimplification). If it is working correctly, you idle well as long as the ecu gets the throttle-closed signal from the TPS.

A significant vac leak coupled with a significant vac requirement to refill the brake booster temporarily upsets the volume of air going to the motor and the IAC needs a second or two to compensate.

Likely your vac leak is the line to the booster, the check valve on the booster or the booster itself but I did not want you to zero in on that one stream to the exclusion of all others.

If either line to the IAC has a leak, the IAC is unplugged, the line to the flame trap (probably too small), the line to the climate controls or its check valve, the line to the evap canister, the line to the cruise control, etc...any of them are bad and it could be your culprit.

There is also the chance it is something else but your specific series of events screams vac leak.