Does the I terminal not provide power any more once the engine is done cranking?
YES. But not full 12V from the solenoid (fender relay). If you look at the
wiring diagrams for your '65, you'll see the RED/GRN ignition wire splits at the firewall to the coil(-) and the "I" terminal (BRN wire). They are joined. So, while cranking, un-resisted full-power feeds from the "I" terminal to the coil(-) for increased starting spark power.
When the key moves to RUN, the solenoid disengages, stopping full 12V feed. However, the wires are still joined at the firewall, so coil(-) power still flows to the "I" terminal, which is now a dead-end. Fortunately, it is still hot with power from the PINK resistance wire, and makes for a point we can tap for the relay 86 terminal. See the opportunity? This is what many refer-to.
Having said all that, I do not suggest the "I" terminal to energize the relay, unless you test the relay for voltage required for energizing, and drop-out (relay release) voltage. The issue is that the power on that BRN wire (except when cranking) is not full 12V, more like 6 to 7.5V, and standard 12V Bosch-style relay operation at low battery voltage (terminal voltage down to 5V or less) may not be reliable to hold the relay ON when the key moves to RUN.** My preference is to avoid the resistance and just pull power directly from the key switch "C" terminal, or the RED/GRN wire from it,
before the PINK resistor wire. This
ensures full battery voltage to the relay 86 terminal any time the key is in RUN or START.
**
Here is an example of a "typical" generic Bosch-style 30/40A relay and specifications from a reputable supplier. Better or more-suitable ones are available with careful shopping, but that's typical with kits and such. Note the "Must Operate" voltage is 8.4V. That's higher than the PINK wire resisted voltage is on the coil(-) wire when the key is in RUN. While it will
probably work, you can see how we are on the edge of unreliability, especially with a low battery when you
really want it to work.