You probably wouldn't need to use a variac if you used a light bulb limiter at first turn on. https://www.instructables.com/Light-Bulb-Current-Limiter/
That LBL will work, but it's way too big.
Use the same double steel outlet wall box but
with rounded corners, use the deep box version so you have room to fit the outlets/switch. Get the 1 that takes the exposed work metal cover, screw holes for metal cover are in a different place. Don't get the metal cover that extends past the box, that's a wall plate cover. Go to a big box store and make sure the cover fits the box.
Then put in a single on/off switch and a duplex (double) outlet, both in the same box. Then use a single light bulb plug in socket for the light bulb. (Like in the drawing below.) Much smaller package. Make sure to use a 3 wire power cord and ground the 3rd green wire to the metal box. And use a metal box clamp for the power cord.
Remember to break the tabs off both sides of the duplex (double) outlet.
Some guys like to add the switch, so you can switch between current limit and regular ac wall voltage without unplugging the amp from the LBL box.
You want a 60w bulb for small amps, 15w to 20w, and 100w bulb for larger amps. I use a 40w bulb for little 5w SE Champ amp types. Don't use a 200w or larger bulb. The lower the wattage the more protection the bulb will give. Has to be a real steel filament. Can be a halogen.
And you don't use the variac with the LBL. Once you find there's no shorts with the LBL, you don't use it anymore. And you can't take any voltage measurements while the plugged into the LBL, they will be wrong.
I can't seem to find pictures on line that have the right file extensions to post here.
You don't need the on/off switch, or the IEC power cord socket that are in the drawing below.