Tachometer works sometimes and won't work others, plus the right turn bsignal blinks rapidly ; what is the cause and how to fix

SOURCE: turn signals blink on the wrong side

Do you have a trailer hitch? If you do, the problem may be in the wiring for your trailer lights. I use to work for u-haul and installed $75,000 worth of hitches in one year. the vehicle in your picture take a power module to work your trailer lights. this means a device that takes power from the battery to make your trailer lights work, if you hook up trailer lights to the existing vehicle wiring it will cause a lamp-out sensor failure. If you have this wiring check for normal operation with a test light. If you go to u-haul they probably will inspect your wiring for free. If the device was installed properly, it still can malfunction and probably will sooner or later due to condensation inside the power module. I replaced many of these while working for u-haul.

SOURCE: tachometer gauge

your relay is going bad, replace it.

SOURCE: Power Locks

A motor in one of the doors was going bad and had not completely quit. The dealer replaced the motor in the sliding door behind the driver's side and now the locks work fine after several trips to the dealer and several "reprogramming" issues. The service person also told me that this was not new. Occassionally before a motor goes completely out it can make the whole locking system fail. I am one week without the problem now!

SOURCE: Corolla 2002 tachometer back light

Get a GOOD small Phillips screwdriver and remove the plastic screw in the middle of the meter hood sub assembly. You may have to hold the outer plastic ring of the screw to keep it from spinning. Sometimes they are hard to get out,(try not to push up on the screwdriver and once it starts to come out you should be able to pull it the rest of the way). See pic circled in red.

Carefully pry away between the sub assembly and the upper dash with a flathead screwdriver wrapped in masking tape. Once it is movable lower the steering wheel all the way down and pull the sub assembly out.
Remove the Phillips head screw on the top of the meter combination assembly. At the bottom of the assembly you will find two little metal tabs, push each one back gently one at a time while moving the meter out. Disconnect the two plugs at the top of the assembly. Once removed I would replace all the lights. Why do this again?

SOURCE: TURN SIGNAL BLINKS TO FAST RIGHT

The blinker usually blinks fast when a turn signal light is burnt or not contacting. Check the signal bulbs to see if they are contacting or in good condition. If that is not it. Try replacing the blinker under the dash.