You bought a pair of 21 Watt LED bulbs? You are definitely planning to melt the bushes. A couple of points, though. First, are they rated for AC as well as DC, or only for DC? Second, remember that they use the same amount of power as the original incandescent bulbs that were in those lights, they just produce ten times more light when they do it.
Did you get the correct type of bulb base? There are twin filament bases, with two solder terminals on the end of the base and either symmetrical or offset pins for the bayonet base, similar-looking single filament bases with two solder terminals but only one of them connected, and single filament bases with one central solder terminal and symmetrical pins for the bayonet base. If you have bought single filament bulbs with twin solder contacts, you may not have been applying power to the right contact. If you were forcing a symmetrical-pin single contact bulb into an offset-pin twin contact socket, anything could happen.
That plastic fitting on your engine looks like the mounting for a voltage regulator. Since you did not get a large, regulated alternator, nobody installed a regulator in the mounting.
