Which fuse runs the windshield washer pump on 98 Toyota Corolla?

Not easy to get to, but you can do it with basic tools. It requires removal of the front bumper. Here's a video tutorial on how to access the washer bottle and pump -
How To Install Replace Windshield Washer Bottle Toyota Corolla 03 08...

One hour plus part.Find should say windshield washer.

check the pump it is located on the bottom part of washer tank

Disconnect socket going into washer pump.Check to see if the power supply at pump is there by testing with a circuit tester. Pull back on wiper washer switch to perform this.If you have power its the pump.

Check in the engine compartment on the driverside. There is a black fuse/relay box.
Also the washer tank pump could be broken.

Can you hear the pump working when you try to wash? If no, check for voltage at the pump (usually located under the washer reservoir). If there is voltage but pump doesn't operate, replace pump. If no voltage, check fuse or problem is switch in steering column.

I assume that you are talking about the windshield washer pump. The fuse for the washer pump is the same as the wiper fuse; they share the same fuse. If your wipers work, and your pump does not, you ned to order a washer pump and replace it. Easy to do; just unbolt the bottle, raise it up, yank off the old pump and pop the new pump on.

There is a fuse for that. Do you hear it? Is it empty?

You seem to have the motor not working or there is not any power going to the washer pump motor. Check the fuse in the box first.
Ken S.

there no fuse for just the washer it has the wiper on that fuses if you press the washer and wiper start its not the fuse it a bad washer pump pierre