It works fine in the protoboard, with 5, 10 or 21 W bulb (didn’t test it with more than one of such bulbs tho), however when I connected to a car’s (a clunker, may I add) turn indicator harness, it does blinks but the MOSFET gets very very hot. I didn’t run it for too long, perhaps 20 blinks and it was untouchable…why it got so hot?
I used an IFR630, 200V 9A N-channel MOSFET. Four 12 V/21 W car bulb may be consuming around 8 A. I didn’t test four at once but only 2. Could it be the car's harness loose ground, or positive to ground leak? Or it just can't handle the load? From the site I got this schematics, people say it worked for them just fine.
UPDATE: I have tried quite a few changes, many of these guided by the brilliant answers here, and once ok in the simulator I assembled in the breadboard for a test. They all worked fine as long as I don't add 21w x 4 + 2 x 10w + 2 x 5w bulbs as a full load test. All of the Mosfets I tried, both n and p, both on high or low sides turned into bread toasters! So seems a no-go project and instead decided to build a simple relay blinker using just a pnp transistor as driver. Of course, it works ok with all that load, since the relay power contacts can handle it. Not what I wanted but...well...works.