Chris;

An Ignition Condenser should be located at Distributor to quench Points. What node is Condenser at Coil connected to...if +, then it is strictly an (additional Condenser) for filtering Ignition Noise...

If Tach is reading, wire is clearly being "sensed"..."connected" is not the right term...no electrical connection or termination is made to white Points wire at Tach...there is only a magnetic one (in a wire loop between Ignition Coil and Points) to allow instrument to sense ignition pulses...this is by design...so that no failure of Tach, can disable Ignition (short of compromised insulation anywhere on White points wire, allowing a connection to chassis - which would result in your symptoms BTW!).

"dangling down by the distributor" ??? ...connected or not and to what???

I suggest you check wiring and return wiring to stock...if wiring is something other than stock (and you don't advise this), I can't help you.

Good Hunting!