Where is the relay switch located on the 98 lincoln navigator for the turn signals and what is the relay switch

may be flasher relay, links which may help

(5) Navigator flasher relay replacement - YouTube

2003 Lincoln Navigator - Turn signal blinks just a few times (repairpal.com)

SOLVED: 04 navigator flasher relay location - Fixya

Fuse Box Diagram Lincoln Navigator (2003-2006) (fuse-box.info)

That's right they are replaceable
http://www.partsgeek.com/624mgf8-lincoln-navigator-door-contact-switch.html?utm_source=bing&utm_medium=ff&utm_content=MP&utm_campaign=PartsGeek+Bing&gb=pp&utm_term=98+1998+lincoln+navigator+door+contact+switch+-+front+dorman+door+contact+switch&ad=11620898073

ford f350 door ajar switch fix 99 expedition

It doesn't have one Controlled by smart junction box .
The smart junction box (SJB) monitors the multifunction switch position by sending multiple voltage reference signals to the multifunction switch. When the multifunction switch is in the LH or RH TURN positions, or the hazard lamp switch is pressed, that input signal is routed to ground.
When the SJB receives a request for a turn signal or hazard lamps, the SJB supplies voltage to the appropriate turn lamps.
The timed on/off cycle is determined by the SJB and is set to flash approximately 80 times per minute if both the front and rear turn lamps operate correctly. If an individual turn signal lamp is inoperative, the SJB flashes the remaining turn lamp approximately 160 times per minute.

Taryn, sounds like a faulty turn signal switch, or multi function switch is defective. Check all the bulbs and sockets first for damage wires, burnt wires or bulb socket, cheapest part to change besides bulbs would be the signal flasher or the signal relay if you want to go this route. Below are trouble shooting links you can read or watch.
press the helpful button and follow me on fixya for more tips

Turn Signal Switch May Fail and Cause Clicking Noise Chevrolet Tahoe...

How To Change Turn Signal Wiper Control Switch On Ford Lincoln Or Mercury

How to Replace Your Turn Signal Relay in Lincoln Navigator eHow

Blinker light flasher change out on 2003 Ford Expedition

press the helpful button and follow me on fixya for more tips

I think you should reset the ecu system. Hope it works!

Contrary to other posts, the 03-05 Lincoln Navigator turn signal flasher relay is not above the ODBII diagnostic plug above the accelerator. It is in a plastic box that is located six inches above the hood release lever. The plastic cap can be prised off by wiggling and pulling up. The flasher release is the larger of the two in the relay module Due to placement, this has to be done entirely by feel.

I am not 100% sure as far as on a 98 navigator, but I had a 99 Ford Explorer which is pretty close. My relay was under the hood in a box located near the firewall in front of the drivers side. Other cars I've had, have had them under the dash on the drivers side. You have to get on your back and lool up in the wires for a round lookin relay or it may be square. Either way, those are the only two places I have ever known them to be on any car. A flashlight will help greatly. Hope this helps some.

Could very well be faulty relay, bad fusible link, or a fuse in general. You can trace the wiring or view a free repair manual at autozone.com to trace wires to find faulty device. You can use an ohmmeter or multi-tester to test relays and fuses.

Thats strange they should be on the fuse panel ! Are you sure !!!!

sounds like
turn signal relay