My guess is that when you push the shift lever all the way over to the left to grab Second, the lever can go (currently) just so far and then hits up against the left side of the lockout plate. This prevents the lever from properly positioning the shift rod and the hockey stick inside of the transmision to fit into the second gear slot.
First and second are shifted by the same rod within the transmission, so it is usually easier to get it into one of those gears and then move it into the other.
But not in your case.
It needs to go just a hair more to find second, but just for second, which tells me that the base of the shift lever (or maybe just the lockout plate) is not positioned exactly straight front to back and that slight angle means that the shift rod is rotating more for one gear (1'st or 2'nd) than the other.
Try loosening the front bolt just a little, so it's still snug, and the back one slightly more loose than the front but still snug, then, using a flat punch or block of hardwood, tap the rear of the shift lever base so it moves to the Left about 1/16". Re-tighten both bolts being careful that the base stays put and try a road test.
This is often an iterative process - change something, road test, change something, road test, kind-of-like tuning in a radio. Go slow, be patient and I think you'll dial it in.
I mention moving the base to the left, but it may be happier with a move to the right. Play with it and I'm sure you'll get it.