Yup, looks like new LEDs draw less current than factory lights, so relay flashes too fast.
Resistors are meant to be wired in parallel to increase power consumption to trick relay into working like original lights were installed. LEDs consume about 2-watts and incandescent bulbs about 20-watts. So resistor in parallel consumes additional 18-watts for 20-watts total. It basically operates like invisible bulb that converts power to heat without putting out any light.
Here's difference between wiring resistors inline/series vs. parallel::
With inline/series connection, total resistance of circuit increases and less current flows, and less power is consumed. That's why your light doesn't turn on at all, resistor blocked power that should've gone to light.
With parallel wiring, resistor forms 2nd independent circuit that doesn't interfere with original light at all. It lowers total resistance of circuit and consumes additional power: That's also why flasher works properly in hazard mode, second set of lights in parallel doubles power consumption.
Here's how to wire up resistors in parallel to increase power-consumption. Make sure you use higher-resistance resistor meant for LED-to-LED conversions.
Basically resistor in parallel circuit connects to both wires of light. Be sure to solder and wrap connections for good conductivity and seal out moisture. Otherwise you'll have to redo this in couple of months when it falls apart or corrodes.
I can post some maths to show how this works if you'd like. Can even calculate exact value of resistor (ohms) needed for any kind of factory light vs. aftermarket replacement.