[Kube]

My first piece of advice is to NOT splice. Rather, replace the harness. If splicing is necessary, it makes me think the harness is old and becoming brittle (not safe).
If you insist on splicing, solder the connections and use heat shrink tubing. Both easy to do and far superior to tape.
Those "tubes" you mention must be hard as a rock for you to see them as Bakelite. They are rubber sleeves over the metal connectors within.
Yes, from your description, I must ask you to please replace the harness. Your car is too nice to chance old, unsafe wiring and connections.
I'd recently purchased harnesses from Mike Driskell. Reasonably priced, shipped quickly and very good quality.