Replacing the ignition switch will be a good starting point, if that doesn't solve your problem you will have to start one point and check the whole harness for breaks or bad connection points.
1983 Honda ATC250R
1983 Honda ATC200E BIG RED (sold)
1984 Honda ATC200E BIG RED
1984 Honda ATC200X (sold)
1985 Honda ATC70 x 3
1985 Honda ATC250ES BIG RED
1988 Honda ATC250ES BIG RED
1995 Honda Frankentrike 50cc 2-stroke
2001 Honda TRX90
2004 Honda TRX300EX (sold)
2008 Honda TRX250TM
1976 Suzuki RV90M (sold)
1967 Vespa Primavera 125
1958 Massey Ferguson 35