I would respond kindly to all of your "thank you" emails.
If I were on the demand side...
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But then a few days after my no-response your feelings will get hurt and then you will start another thread on this forum. Hey, we're pretty indifferent to receiving your thank you notes. So unless you send a non-form-letter thank you, don't expect a response. We're all good.
I would respond to your response. I would say, "Thank You for your Thank You note for my Thank You note. I hope to hear from you soon."