Where should I expect to find the trap for my in-wall washing machine drain?
It's going to be below the opening in the wall - most commonly, directly below, which means that if you pull out the washer drain hose and insert a long, slightly flexible rod, you should feel  it hit bottom in the trap, and can make a mark to measure where the trap is with respect to the opening in the wall.

If you are concerned that it might be an elbow rather than a trap, be sure the rod is dry and wash has not recently been done so you can see (or not see) the waterline of the trap on the end of the rod.

And, ultimately, you can always rip open drywall and repair it (an unfortunately common method the way services are installed in houses.)

Personally, I'd suggest giving a try to leaving it where it is, if you have not - there's some sort of cultural tendency to put laundry in the basement, as far from where it's generated and stored as possible. It's worth questioning, and saves a lot of hauling if it's near where most of the sheets, towels, and clothes are used and stored. If moving the machine, I'd suggest leaving all the plumbing in place and putting a test plug in the drain opening, rather than removing the plumbing - a future owner of the house might appreciate it, and it's less work.