01 ford escort turn signal lights all stay on

Start with checking the brake light switch.
follow the brake pedal up the metal arm until you see a little switch pressed against the metal arm.
When the brakes are pressed, the switch button extends and unlocks the shift lever and turns on the brake lights.
It is common for a little plastic piece to deteriorate and break away, causing the brake lights to stay on and can damage the shift lock solenoid.
Attached is a photo of the brake switch where it contacts the pedal arm.

There is a little snap cover beside the shifter. You can pry it open with a little flathead screwdriver and insert a thin object inside to release the shift lock and get out of gear until you find the fix.

The 98 Escort is actually a Mazda 323 with Ford trim. It uses a solid state flasher relay for both turn signals and hazard lights.
The relay is behind the speedometer. My guess is the relay has died.
You can look it up online or check with your local auto parts store to get a visual.

You have a bad ground to one of the bulbs that is a twin element(one filament fed from the running light circuit,one from the turn signal/brake circuit).Turn on the running lights,and remove the bulbs on that side one at a time.When you pull the bulb that makes the turn signal on the dash go out,that is the socket you need to check.(the ground terminal at the body is probably corroded).Remove the securing bolt,clean the area it's attached to and the terminal,and bolt it back in.You might want to add a "star" washer between the terminal and body-it bites into both surfaces and assures a good connection.(I DON'T see these "experts" on the various car shows doing this,but what do they care since they probably get rid of these cars as soon as shooting is done?).

The turn siganl switch because the brake lights go through there. Otherwise, turn signals would not work with brakes on. 4 way flashers should work though

It is the light box. You know the pulley you use to turn lights on and off??? that goes bad all the time. Replace that and your gold.

A BAD BULB MORE LIKELY.

it sounds like your flasher is going out and if not that then it could be a short in the system

check the breaklight switch it might be stuck its on the top of the break pedal...

It's probably a stuck brake light switch. Look around the brake pedal for the switch -- it could be dirty or broken or loose from its mount and jammed against something.

You broke your serpentine belt. These are cheap and easy to replace for the most part. Usually you can do them yourself.

Sincerely,

JC