If you just want to get it running, you don't need an ignition switch.
In 1987 there were 3 models of TRX250's. The TRX250 (electric start), the TRX250R (two stroke) and the X (kick start).
The R and X are easy - just unplug the ignition switch and ensure the Black wire with the White stripe is not shorted to ground at the CDI unit. If all is well in the ignition system, you will have spark. The electric start model requires that you unplug the key switch and jump the red to the black wire and make sure the Black wire with the White stripe at the CDI unit is not shorted to ground. The reason for jumping the red to black wires together it so energize the electrical system so the electric starter will work. Of course, you will need a battery to spin the starter. Otherwise, just unplug the key switch and push start.
Once you get it running, then you can worry about tires.
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