Miswired smaller transformers may not
draw enough primary current to trip the breaker, as the fine wire of the primary can fuse at the leadout or an internal thermal/overcurrent fuse can blow before the breaker trips.
I don't have any decent sized mains transformers hanging around at the moment so I grabbed my 250VA portable isolating transformer (toroidial 240V, 1A), took the plug off it and put a batten lamp holder in series. A 100W bulb didn't glow at all. A 40W bulb flashed dimly with the initial surge current then didn't glow. Unfortunately I don't have any lower wattage mains incandescent bulbs.
On a cheap DMM's 10A range the surge flicked up to several hundred mA then the magnetizing current very rapidly dropped away below 10mA, the limit of its resolution. If I'd tried a lower current range the surge would have almost certainly blown the multimeter fuse, so I *DO* *NOT* recommend attempting to measure the magnetizing current in the field with a DMM.
If you want to do it on the bench, either use a 5 digit or better meter on its 10A range and don't use a transformer over 250VA, 240V or 120VA, 120V (allowing for an x10 surge at switchon, unless you have an essentially free source of meter fuses!
) or rig a shorting switch across the ammeter that you can close before power on, and when changing meter ranges, only opening it to take a reading.
Scoping the magnetising current is a whole different ballgame. There's little point of doing so unless you are investigating transformer design and core saturation. You'll need an isolated current probe and an isolated HV differential voltage probe to see the phasing with respect to the supply voltage. Trying to cheap-skate it without the proper probes is likely to result in the death of your scope, and yourself if careless. An expert engineer can build suitable probes but their design is not really a fit topic for this forum as due to the Dunning–Kruger effect, presenting such a design is an attractive risk to all the idiots who shouldn't be trusted to even wire a plug.