Bill,
In the Commonwealth of VA, it is required by law to have a written "Buyer Agreement", signed by the buyer and broker when the search begins. Your agent is late in getting this to you, but a written agreement is required. The agreement has to have a start and end date, and spell out the terms of the agreement, but of course most of the terms are negotiable.
You could make the term for one day, one week, one year, etc. You can also make it for one property, or properties in a certain area, etc.
If you have seen properties with other agents, I'm surprised they have not requested you sign an agreement.
Most agents use the "Exclusive Right to Represent Buyer Agreement" which states that you have to work with that agent and no other during the term of the agreement. Another option that may work best for you is to ask him if he is okay with using the "Non-Exclusive Right to Represent Buyer Agreement". This will give you the right to work with other agents at the same time as long as the other agents agree to use the same form.
I hope that helps you.