I will make a guess at some of the contents of your junk box. Shoot me an email if I messed up.
IRFZ44N power N-fet would be great for 1.25A.
The Gate goes where the Base is shown in the diagram.
The Source goes where the Emitter is shown in the diagram.
The Drain goes where the Collector is shown in the diagram.
Change R5 to 51K or 100K.
The 12V LED bulb replaces the relay in the circuit. + to +, bulb - to N-fet Drain.
D1 1N4001 can be left out.
If it does some excessive blinking before fully committing to On or Off, try a 180K or 220K between pin 6 and 2 on the LM741.
Only 2 more days until the next Harry Potter movie is released.
I wonder if that is a sign?