Grammar question

As a real estate legal secretary, I have sometimes had to type this phrase:

“Landlord and tenant each agree to hold the other harmless . . .”

Should the verb “agree” agree with the plural group “Landlord and tenant” or should it agree with the singular word “each”? Let’s see, the other way would be:

“Landlord and tenant each agrees to hold the other harmless . . .”

I’m betting on the first rendition above, but I’m not 100% sure.

I think it sounds better the first way, although I wonder how it would sound to you with “both” replacing “each”

I gues if you use “each” then it has to be agrees but if you modify the sentence to use “both” then you could use Agree.

I agree with you. I believe the subjects (thus the dominant part of the sentence) are the nouns “landloard and tenent”. Thus the verb needs to agree with them. “Each” in this case (I think) is an indefinite pronoun used as a clarifier to establish that the action is done in agreement (in reference to the compound subject) but separately. To a certain extent I question the need for “each”.