A brahmavadi is one who is tattva-vit, as defined in the shastras:
vadanti tat tattva vidas
tattvam yaj jNaanam advayam
bhagavaan iti Sabdyate
Those who are tattva-vit understand that the Absolute Truth has three nondual features, namely Brahman, Paramatma, and Bhagavan. The mayavadis on the other hand say that the Absolute Truth is Brahman alone, and that Bhagavan is simply Brahman covered by illusion. Therefore they are known as the maya-vadis, because they believe Brahman gets covered by illusion.
Brahmavadi means one who understands that all three features are the nondual Absolute, and he is therefore attracted to the Brahman feature. But such a brahmavadi never commits the offense of saying that the Bhagavan feature is coverd by illusion. He perfectly understands the three features of the Absolute Truth to be nondual and non-material.
ekameva adviteeyam brahma
“There is certainly only one Brahman, there are not two”.
This Brahman is described by Krishna in the Bhagavad-gita:
mayatatam idam sarvam jagad avyakta murtina
mat stani sarvabhutani na caham tesvavastitah
The Absolute Truth does have form, but Krishna says “avyakta murtina”, it is His unseen form. Therefore Brahman has form, but we cannot see it because we are in duality. The spiritual form is beyond our material vision.