Tumblr is high traffic... million people are visiting Tumblr monthly.
There are many methods to monetize... affiliate programs and CPA.
For making money in Tumblr, get more targeted followers... and regularly add contents into your Tumblr blog plus hastags.
Adsense is great, and I use all the traffic to send it off to my site which is also monetized with other methods. Pretty simple.
Don't adsense ban you if you have multiple websites?
Just pick something and try it out.
Everyone wants hard and fast answers in this game, but there are none. Try something, does it turn a profit, if so, scale it up.
the PPC game will get you cents, but cents scaled turns into dollars.
Or squeeze users off tumblr to sites you control, where you are not limited by TOS of tumblr. Offer them something for free in return to join your mailing list, then hit them hard with all kinds of offers, whatever you are pushing
Putting ads on a tumblr is not a good idea these days, but people do it. If you can profit before you are banned, fair play, scale it up.
Others go the followers route. Ran a legit blog, get 10s of thousands of followers, then make a post pushing something.
If using the blackhat way. Having hundreds of tumblr blogs and a couple of your site to send them to. Will tumblr give a red flag saying why these handful of tumblr site has blogs pointing to this one site?
I'm not a huge fan of Adsense for monetizing. Selling posts on your aged, high page rank Tumblr might be a better solution.
As for why Adsense might not work, the average Tumblr user might be immune to Adsense ads and will resist the urge to click ads as most would just prefer to stay on Tumblr rather than going off site.