Wiper delay relay only kicks in when you pull back on the lever. Check your stalk for ground and dirt. Clean that up first.

Next, check your wiper motor. On your car you have a separate switch. If the wipers work fine every time with its own switch then it's not your motor. Although I recommend you take your motor out, open it up and relube it fresh. You'll find the wipers work much better and faster afterwards. You might as well do this now since you are servicing your wiper system.

The washer pump and delay relay share ground so it sounds like you have continuity going all the way through. If all of the above is fine it probably really is your delay relay. Probably stuck in open or close position.

Your car should have the big plastic square relay in it. They come in a 2 speed relay form and an optional 3 speed intermittent. I could show you how to test using the old cylindrical units (3 prongs only) but that won't help you on here since you have the new one. They can be tested on or off of the car. I would look up the procedure in a Haynes manual if you have one or maybe a fellow FAQer can post the test procedure for the newer relays.

On the old relays all you had to do was remove the relay, connect power to terminal 15, ground to 31b and put a 12v test light on M. It should come on and off intermittently every 5 seconds or so. If it stays on or doesn't come on at all you know the relay is bad. You can do a similar test on the newer units if someone here can post it. I don't have any manuals for anything past '72....

good luck.