You can always check to see if the sprayer head is plugged up by removing it and washing it etc. But, probably you have a leaky seal in the compression fitted top. I had the same problem with a vintage bottle of fragrance and after trying lots of things to fix it ended up selling it to my favorite fragrance decant reseller (PC). They will pull the top and remove the juice anyway so it was perfect for them.
The only real way to fix a faulty sprayer on a mechanically sealed spray top bottle is to pull off the top completely and replace it with a new one. If you can find a local fragrance bottler or someone who has the right tools to put a new fitting onto the bottle they could fix it easily for you. I was not able to find someone with these tools. I looked all over too, but no luck here in the midwest.
There is a need for a fragrance repair service for fragrance bottles that leak and have gone wonky. A common problem with the older vintage spray bottles!