On the Eurail website you can't choose seats. They will be assigned automatically.

You can choose seats on www.raileurope.com (Desktop website only).

Thanks for the response but, I am on the desktop at  www.raileurope.com now and do not see a way to book reserve seats only (no ticket).

There is an option "Add rail pass”:

Thank you!

Got my seats booked. :)

How long does it typically take to receive a confirming email from raileurope.com after the purchase of reserved seats?

It was pretty fast for me, maybe a few minutes. Did you check the spam folder?

Has been 2.5 hours. Nothing in Spam. 

Did you create an account? You could log there and get the PDF too.

Were you charged?

Was charged, no email confirmation (checked spam).

Checked my raileurope.com account - nothing there either

I guess then it's time to contact their customer service.

Response from customer service (took about 10 hours):

I apologize for informing you that the seat reservation you attempted to reserve was not fulfilled.

Since the reservation was unsuccessful, I've asked my team to revoke the payment. It will appear in the account after five to ten business days.

You will need to book the seat reservation using the Rail Europe website and add that you have a rail pass while searching for the segment. “

I tried to book the seat reservation again and it went through without difficulty.

AND, I have already received credit for the refund at my bank.  :)