Its the pipe itself, it needs to be removed and rebuilt by enzed. I've had a couple done now and it's generally about $80 from memory.
Very common minor fault on the Celicas, the guy at Enzed said they do about one a day!
You don't need to drain the fluid as most of it is held in the resovoir but you will still get some leaks when you remove the pipe so have some rags handy, and replace the two copper washers either side of the banjo bolt that holds the pipes fitting to the pump.
If you ask real nice I should be able to give you a hand with it after new years as it is a royal c*nt of a job if you havn't done one before on a celica.