Do you know easy ways to test fiber optic patch cords that don't require equipment test?

Shine a light in one end and if it comes out the other side it's working.

I assume you have access to a managed switch or router with the correct type of interface, single or multi mode.

I just loop the connection put the cable on the optic module and connect the ends with a loop back block or you can use a connector and connect them with a known good cable.  I like to use a loop back block because you use both sides at one time, or you can simply test one at a time by  plugging one (if not duplex connector) from the TX to RX ports.

If the interface lights up, then the cable is probably good (at least it has no errors, it might still be dirty).

Point one end towards then away from a light source and check you see the change in illumination at the other end!

As long as they are commercially made & terminated fibre cables (not home made) the only likely problem is a cracked core, which should be very obvious in low or no light through in comparison to good ones.

If you are making your own, then termination and polishing are absolutely critical and you must use appropriate tools and follow the connector makers instructions for fitting the connectors & any polishing stages.

No!