Most of the tandem focused dealers usually have a bike or 2 they will rent, however, you have to be lucky enough to live close enough to make it worth while. A simple google search will help you locate them.
I completely agree that borrowing or renting a bike to try is the best first step. Trying the wrong bike could result in a bad experience and steer you away from a lifetime of enjoyment. Here are a couple of suggestions: Reach out to your local bike clubs and asking if there are any tandem enthusiasts. Many of us serious tandem riders have more than one bike and are usually happy to help a first time team try the experience. Also, they are a wealth of knowledge for both captain and stoker.
A used older "better" bike is preferable over a new cheap heavy one.. Spending some time on eBay and Craigslist and you will quickly see what is selling and for what (always check the already sold listings in eBay). You can always ask on this board about a specific bike. If you have never tried it, google "search tempest" which will allow to easily set up a Craigslist (and eBay) searches for anything you are looking for that covers a large geographic area.
Here are 2 tandem specific online classified sites:
Tandems east:
Tandem Bicycles For Sale, Tandem Bike Components For Sale
A used older "be Tandem club of america:
https://tandemclub.org/classifieds/browse-ads/
Don't let the prices scare you. Tandems can be expensive but with some knowledge and a bit ot time, excellent values can be found.