ORIGINAL: cutaway
Modern commonly available dimmer switches use a device called a triac which chops the duty cycle of standard 60hz house current. They don't operate anything like the old school rheostat. IOW, they they don't reduce current or voltage in the usual sense, rather they shape what was a sine wave into short voltage spikes with an elongated long delay between the spikes. I don't even know if they'd work properly in a DC environment.
The dimmer will be on the primary side of the transformer, so will only see AC voltage/current.
EDIT;
My 24 volt transformer turned out to be a 230 volt primary. So I'm back to square one with my original 4 amp battery charger.
I hooked up a light dimmer last night and gave it a go. I also stuck an amp meter in line to see what was going on. Full bore was a 9 amp draw[X(] No wonder the breaker was tripping!. Dialed back to 5 amps, it would hold for about 60 seconds, but the wire is to cold for a good cut. I'm using wire from an ice machine cube cutter. I've had it for years and it worked fine with my old power supply. Off to find new wire today.