You would require both trustees to sign the signature card to make certain the other trustee is aware of the account's existence and that it does not serve as a vehicle to divert payments made to the trust. Since you are empowered to act independently, it's fine that you are the only one who signs the checks, but the bank won't want to deal with a disgruntled trustee who claims not to have known about the account at all.
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In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.