Are you planning to use a Transformer with single windings on both sides [Primary and Secondary]? And this Transformer is rated only as 240 Pri / 24 Sec.?
If the Volt-Amp rating [VA or KVA] was 250 VA for this Transformer, and you plan to drive it at 120 VAC, only load it up to 125 VA. Otherwise it will burn out.
125 VA @ 12 VAC would be around 10.3 amps.
Falling under the 125 VA rating assures the smoke remains inside the windings
If the transformer has "Split Windings", then connect the windings as needed to be driven from 120 VAC and output of 12 VAC.
If only one side has split coils, leave the arrangements as 240 VAC Pri / 24 VAC sec.
I used a very large rating for a Control Transformer [250 VA]. They are usually around 25 VA min. to 100 VA max., with 50 VA being a normal rating.
If you plan to drive an Automotive Headlamp, you should consider a larger Transformer.