Turn Signal/Parking lamp modification-

I have a two filament turn signal/parking lamp on my car (3157A bulb).
When the parking lights are on, the turn signal is not as noticeable as when the parking lamp filament is off.
I would like to add a relay so that all the while the turn signal is on the parking filament on that side turns off. On my vehicle I have located both wires that ground out constantly (between smart junction box and signal switch) when the turn signal switch is activated.

I will use a normally closed relay for the parking lamp circuit and power one end of the coil (pin86) along with pin 30 to parking line feed from the car. Pin 87a (NC) as the output to the bulb. Pin85 can be connected to the ground of the turn signal, this will act as a switch whenever turn signal grounds it out it will open the contacts and turn off the parking lamps. I will need two relays one for either side. The 3157 bulb draws about 0.6amps for the parking lamp filament.

I need to clarify couple things:

1) Since this is a very low current circuit would it be ok to use a generic automotive relay ie: bosch 30 or 40 amp rated? Is this too high a rated relay for my use? Should I use a smaller rated like one of those 12vdc 10amp or 5amp PC relay like this one https://www.e-sonic.com/ds/505330.pdf?p=45319483
2)Do I need to install a flyback diode in parallel with the coil to prevent damage to other components?

Thanks in advance.