Right front turn signal not working and bulb and connections ok.

try bulb change first if still problem test socket and harness

i don't know. blinker slows to normal when both bulbs work. using volt meter or similar, test rear socket for a
continuity to ground. if OK test socket for 12 volts from
socket to ground. if OK, bulb is not making contact. if not
OK, note wire colour and look for damaged or loose
connection from front. check white back up light as well.

The other turn signals front and rear work ok? Disconnect right turn signal, with that signal turned on, use a test lite on the white wire with lite blue tracer, does the test lite pulse?
Does the right turn indicator on the dash pulse on and off?

If the rear turn signal lights are out, and the front lights are ok but don't blink then, the bad bulbs in the rear turn signals should need to be replaced.
Or there could be a bad ground connection.
Also, there may be two relays for front and back lights.
Hope this helps.

Fast flashing occurs when one bulb in the circuit has failed. If the back turn signal bulb is flashing, then a front bulb has failed. Try replacing any remaining burned out bulbs (there may be more than one at the front and/or the back - if the right side is ok, check that side of the vehicle for locations reference). Be aware that the problem can also be one or more bad turn light bulb socket connections - in some cases, dielectric grease may have been added inside the sockets to inhibit corrosion. This is not usually a problem, but to be sure, make sure they are clean and free of corrosion.

Check the front turn signal bulbs. This will affect the resistance in the circuit and cause the working light to flash at a much faster rate.

No - headlight ok.
The reason that the Right turn signal blinks fast is that there is half the normal load (resistance)
on the right side, since the Right front turn signal isn't working.
Since you replaced the Right front turn signal bulb, your problem lies in the bulb socket or
the wiring to the socket.
(1) try cleaning out the socket - there's probably a contact problem in the socket. You
may need to squeeze the contacts together to provide good contact to the socket contact.
(2) if contacts inside the socket are ok, try back-probing the socket - to make sure that the
socket is getting 12V DC to light the bulb. Replacing a bulb socket is easy, and commonly done.
Any auto parts dtore should be able to sell you a new socket - its just a matter of cutting out the
old one, and then splicing in the new one. Most shops will use small wire nuts, buried under several
wraps of E-tape (electrical tape).
(3) if bulb AND socket ok, you have the worst problem known to man - a wiring fault. In this case,
you'll want to run a new wire from the flasher module (under the dashboard) to the turn signal.

your problem seems to be the turn signal stalk.check the connections are clean and tight,if they are ok then replace the stalk.

Bypass head light switch and see what you get. Three items can cause your problem . The head light switch, flasher relay , shorts in circuit. I would go with switch.

if bulbs okay check fuse is good you got faulty turn switch or bad ground.