Schumacher Cougar layshaft play??

[Don't tell the Mrs]

I'm in the process of slowly getting my first race car running again and have fully rebuilt the gearbox with new parts. All parts are correct and assembled in accordance with the instructions but the pulley on the layshaft has about 4mm of play from side to side. Upon inspection it is the pin moving within the slot in the pulley. Given that it's the best part of 22 years since I last had it running so my memory's not that clear - is that normal or have I got a pulley that's been manufactured incorrectly?