4wd sistem warning light tucson 2005 is blinks while driving

If your model has 4wd, the computer decides when it is needed.
There should be a button on the dash that will allow you to lock it into 4wd up to 30 mph.

i believe its a 2oA fuse.

It could be as simple as your battery, and then a alternator

Check the relay first then the fuse. If they are not bad then it might be that the switch is burned out after that it will be in the shift modulator for the 4 wheel drive. If it is the modulator then you will need a new one.

There are many vehicles which notice same issue with 4wd not engaging in low or high mode.I suggest you few help links related to these issue,with there troubleshooting details and solutions.
Car will not go into 4WD high or 4WD low? http://schematicsdiagram.blogspot.com/2011/12/car-will-not-go-into-4wd-high-or-4wd.html

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No 4x4 light on dash?

http://repairhelpcenter.blogspot.com/2011/12/no-4x4-light-on-dash.html

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4 wheel drive system will not disengage?

http://technoanswers.blogspot.com/2012/01/4-wheel-drive-system-will-not-disengage.html

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4WD light is flashing and beeping? NO 4WD high?

http://schematicsdiagram.blogspot.in/2012/02/4wd-light-is-flashing-and-beeping-no.html

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2002 Jeep Wrangler: 4WD Idiot Light is ON?

http://technoanswers.blogspot.in/2012/06/2002-jeep-wrangler-4wd-idiot-light-is.html

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Traction control switch will not engage on 4WD High or Low
http://whoisbyme.blogspot.com/2012/10/traction-control-switch-will-not-engage.html

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Service 4wd warning light on Dash? http://howtobyme.blogspot.com/2011/11/service-4wd-warning-light-on-dash.html

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Car automatically switches to 4wd low?

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These are the help links related to your issue.Going through these help links,will guide you to troubleshoot and solve the issue noticed on your car.
Keep updated for more help.
Thanks.

http://www.tradebit.com/filedetail.php/1593310-hyundai-tucson-car-workshop-service-repair

There may also be a Haynes Manual available, but I have not found one for your vehicle yet.

I’m happy to help further over the phone at https://www.6ya.com/expert/jeremy_69f3cc28d95bf514

Is the battery new or just charged. the battery could be the problem. Check the cables for corrosion or loose connections. The cables can corrode inside the insulation near the battery this can be seen by swollen cables.

Try to charge the battery?

The light blink's to warn its not properly out of 4WD. When the light blink's it is recomended you reverce a few meter's to allow the front axle to disengage.