blinker/parking light wiring

Wiring up new parking lights/turn signals on a project jeep. Problem is I have to wire the 3 wires into a 2 wire socket. So you've got 1 blinking positive, 1 parking light positive, and ground. I got it to work using a diode on the blinker wire and a resistor on the parking light wire but the parking light was real dim. I'm sure I can do this with a relay but everything changes when the parking light is off (daytime) versus when the parking light is on (nighttime). Anyone have an elegant solution?

More info: Front or rear? Brake & flasher combined? New light is dual filament else 2 bulbs?

IF your resister is too high in value, the light WOULD be dim. I use 60ohm resisters for the most part, 330ohm for smaller LEDs. You said you are using a resister on the parking light side, so, it would be dimmer than not using the resister on the blink side.