Asked this in the 80s tech section, but now that I look I think this is a more appropriate place. Browsing the local pick-n-pull, I found an 86 GL turbo hatch with power steering. Will the pump/lines/rack swap easily into my 81 Brat, or will I need to modify/swap the cross member?

No, and yes..... and it's a bad idea to use a turbo R&P unit because the plumbing is all backwards.

 

That's an EA82 body and your '81 Brat is much narrower (2 generations narrower in fact). It will not work without a lot of modification.

 

You might be able to use an EA81 power rack without as much trouble. They are narrower..... but I haven't heard of anyone doing it. You really don't need power steering anyway unless you get crazy and build a tranny with a front LSD like I built for renob123.... that Brat could use power assist. Otherwise it's not needed for rally-x. Ask renob123 (Jacob) about it - he will tell you.

 

GD