Gene has solid advice and I'm close to the same age (69 & also recently retired). The difference is that I have owned and driven Zs since graduating from college and they have brought more smiles and joy than I can fully express, and certainly more than anything outside of my marriage and family. I'm not sure where that passion originated, but the '72 240Z I bought around your age undoubtedly ignited it.
My feeling is that a good life is all about being in a position to make your own choices. So many people lose that ability because they make poor short-term or momentary decisions that trap them - sometimes for their remaining life. I have been very fortunate to have been able to "have a bit of it all". As I reflect back, there's lots of things that had little do with my actions (starting with the absence of unfairness and tragedy that impacts so many); but probably the most important thing I could control was patience.
So, while you are saving for a house, you can probably also start saving some smaller about for this car. That undoubtedly means being willing to sacrificing other things (dining out, entertainment, etc). You don't need to cut them out completely, but you might be able to reduce by 50%. The point is - it is possible to do both if you are patient to save towards it. Also, you may find that after you've invested the time and delayed gratification, when you've reached the goal where you are able to buy, you will find yourself being much more selective in making a good choice, rather than rushing to fall what looks like the "good deal". There is ALWAYS someone selling because they have to because their trying to escape the trap their in from a short-sighted decision. I was able to get my current 2016 Nismo because the original owner decided it was too small and uncomfortable after 3500 miles.
Oh, and just to provide a small glimpse into the joy that my Z passion has given me, here's a recent pic from certainly one of the best days of my life.
Spoiler