their is no Delta faucet that you pull out on to
either get volume or temperature...that I am aware of...
you are 100% sure its a Delta??
it sounds more like a Moen, if its some odd ball Mixit
then you are in trouble...
post a picture of it and anyone here can probably tell you what it is...
I have delta faucets sitting on a shelf in my building going back into the early 80s .still in the original boxes.
(yea... I collect them).
show me a picture and perhaps I can match it up