Welcome to the show!
Well, grounds are a good place to start looking.
The factory ground to the driveline is a braided strap on the transmission mount. It should go from a chassis attachment bolt to a trans attachment bolt, bridging ground across the rubber component of the mount. Many folks augment that with a battery-cable ground between the chassis and block in the engine bay.
A few questions... have you confirmed that it is a 67 by the serial number? Sometimes titles are dated 'when sold' rather than 'when built', and earlier cars may retain their original positive ground.
Conversion is possible, so confirmation is important here.
The main "hot" (we'll presume positive for now) cable goes from the battery to a starter solenoid at the rear corner of the engine bay, by the master cylinders if it's left-hand drive. From there, it spreads out in all its Lucas splendor to the (2) fuse block, starter, etc.
Once you've confirmed the actual polarity, and ground integrity at the battery and on to the chassis and engine, you can start working along the supply path to see where it vanishes. A trouble light is fine, and convenient for this.
Do you have a manual? (Check out the post for new forum members for info on those.) Check out the Technical Data pulldown menu. There's also a nice color wiring diagram available on the web which can help a lot. Google up 'Alpine color wiring diagram' and it should show up.
Others will be along to help, too. I'm sure we'll get you powered up soon.
Good luck!