No, the turn signals should not have power when the ignition switch is off. The brake lights should have power when the ignition switch is off. There are two separate power sources. As I stated above you should have full time power to the brake light switch and power to the flasher when the ignition is on.

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"It's just a phase. He'll grow out of it." Mama, 1964

1956 Chevy 1/2-ton 3100
1953 Chevy 6100 "The Yard dog"
1954 GMC Suburban Now with a new proud owner.