Hey there Thomas,
The short answer is Magg Spur 17. Sorry i haven't got my maps with me, and brain not in gear.

I'm sure there's other people around here who'll have the specific info.
The track is pretty well marked in most places, but would be a bit tricky in a couple of places in low visibility. It's narrow in spots too, which a bit of a nuisance if you have a large, wide pack. But sounds like maybe you're talking day walk?
There's a more overgrown link track from the Arm River Track to the base of the climb up Pillinger itself, but that's not my favourite approach.
Do you know the Arm River Rd? Now you can only get through to the start of the Arm River Track by taking the left hand turn-off from the Arm River Rd onto Maggs Rd. It's now marked with lots of informal signs / road closed. The Magg Spur 17 turnoff is only 1.5 or 3 ish kms before you get to the turnoff to the start of the ART, coming clockwise round the Maggs Rd loop. Last I saw there was a signpost on the MSpur 17 track (2WD). Go to where the road is blocked by a big log to park. Locate the tape heading off to the right ish of the log, and there's the track.
All a bit garbled, I'm afraid. I love Pillinger. Wonderful views!