Shed outlet is powered from a GFCI breaker in the main panel. I want to add a switched light in the shed using power from the outlet. The outlet is a standard 20a grounded outlet, not a GFCI. No issues with doing the wiring, except I am unsure whether using an ungrounded pull-chain type light fixture will cause a ground fault when switched on. Can I use an ordinary ungrounded pull-chain type light or do I need a light that is grounded to avoid a GFCI trip?
This is a common misconception when using Ground Fault Circuit Interruption (GFCI) devices. GFCI devices do not require an equipment ground to function, they detect unbalanced loads within the circuit using the "hot" (ungrounded conductor) and the "neutral" (grounded conductor).
In a properly functioning circuit, the current on the ungrounded conductor and grounded conductor should be equal.
You can test this yourself, using a clamp on ammeter. If you clamp the meter around both the hot and neutral wires, you should read 0 Amps (If you read anything other than 0, you have current leakage). This works because the current flowing through the wires creates an electromagnetic field, and since the current is flowing in opposite directions the fields cancel each other out.
A GFCI device takes advantage of these principles, and is able to detect current leakage by comparing the current on the ungrounded and grounded conductors.
GFCI performs the ground fault interruption by detecting a current leakage. So when power goes out the hot and doesn't return via the neutral, it will trip, without looking at the ground wire. This is why you can't share a GFCI neutral with a hot that's not part of the GFCI circuit, it will trip when a device is plugged in anywhere on the other circuit.
Therefore, short version, the GFCI should work fine without a grounded device.