I have 3 Giant LaFree and 4 think bikes all missing battery packs. there are 3 terminals used: Positive, Common and Negative. What is Common as when I attached 24V to positive and negative even grounding or the Common terminals all I get are flashing lights.
@cropdusterbob, it took a bit of digging; however, I found an online copy of the Owner's manual for the old LaFree bikes that should be helpful. I think the 3rd terminal is the diagnostic feedback. If you go to the 'How Things Work' page and scroll down a bit, you find that flashing LED indicates an electrical issue, perhaps something other than weak batteries.
Do make sure that the 2- 12V12ah batteries you're using are fairly new and fully charged and see if you get the same response. If it's a controller then it's cheaper to rewire using a standard twist throttle with mated controller as long as the motor is still good. The original LaFree controllers & electronics were quirky.
Thanks to pedelecs.co.uk, there's quite a bit of information about these bikes on their forum. The early Giant electrics, like the Lafree were popular in the UK.
They have a viable link to a service manual for an early SLA powered Lafree Sport which will have some good info for you.
Just a word of caution, our shop has worked on several of these and due to the lack of original parts for an unusual motor setup, these can quickly turn into money pits.