Your mechanic doesn't know what he's doing if he says you need a dropped Pitman arm to center your steering. Most 4x4 trucks need dropped Pitman arms after installing a suspension lift but installing one onto a TJ will usually just create problems like bump steer.
There's nothing tricky or difficult to getting an alignment as good as the latest laser guided alignment rack can produce. I discovered that maybe 15 years ago after thinking front-end alignments were some kind of black magic.
On a standard TJ, the only things can can be done for an alignment is the toe-in and centering the steering wheel. Centering the steering wheel is a no-brainer, rotate the adjustment sleeve on the drag link until the steering wheel is centered.
The toe-in is only slightly more time consuming but if you can read a tape measure down to between 1/16" and 1/8", you can set your toe-in as accurately as a rack can produce. A tire shop didn't believe me when I said my toe-in was right on, that I had just set it. They said they'd check it for free and sure enough, it was right on the spec... they were surprised and said they didn't know it could be done at home and get accurate results either.
The only thing I have checked on a rack is the caster angle but I haven't needed to do that in probably 10 years. The camber angle is not adjustable without installing adjustable ball joints.
Here's the alignment writeup I think Water Dog intended to include.... Basic Jeep Front End Alignment
which is includes how to center the steering wheel and set the toe-in. Setting the toe-in is nothing more than rotating the tie-rod so the fronts of the tires are 1/16" to 1/8" closer together than they are in the rear.
You can measure that between the tires, or get some 1" square tubing and do it like shown below which makes measuring a snap. Just clamp the tubing to the rotor and measure between the tubes at points marked equal to your tire diameter.
Take just the usual care and you'll produce a toe-in and centered steering wheel adjustment as good as the best alignment guy on the best alignment rack can produce