My impression is that in the endgame, most checkmates occur at the edge of the board. It would be interesting to see this "vicar" (placeholder name) attacking a king or supporting other attacking pieces, but it would also be interesting to see it create an "artificial edge" that other pieces could drive the king towards. Currently a rook, two knights or two bishops can create a wall of threats the king cannot pass through. Due to temporary colour-confinement of this piece when attacking (like a single knight) the pressure it generates would be still be permeable.
If a knight is diagonally adjacent to the vicar, it would create a solid wall of threats on one side, whereas a pair of knights creates two solid walls of threats. Given that there is usually only one king and no Mann (non-royal king) units, I think one wall suffices.
An opposite-coloured bishop has several opportunities for forming a barrier to king movement if it works with a vicar. A like-coloured bishop could always protect a vicar against the king (or other pieces). Given the vicar isn't colourbound, this might be an effect pairing for endgames, since this versatility allows the combination to shift between attacking and defending. Writing this I'm imagining the vicar out in the open in attack-mode however, rather than imagining it having to protect a chain of units connected to the edge of the board (or that these units themselves might restrict movement of an opposing king).
I'm not sure if it would be too strong if it were allowed a kind of "fast movement" along the edges of the board. Currently, I feel its wazir-movement makes it too constrained for midgame attacks. Late game it wouldn't be an issue since it can still keep pace with pawns. The fastest natural values would be something like "moves as a rook along the edge of the board", or "moves up to half the length of the board as a rook along the edges", or "moves to any position along the edge of the board as long as that movement is contiguous and uninterrupted". The first option of these three feels the most natural given our familiarity with conventional rooks. The final option would make this piece practically faster than both bishops and rooks in many endgames.
Another factor I'm interested in are pieces that have values that scale moderately with board size (eg from a 6x6 to a 16x16). I would expect this piece scales between a bishop and a knight over this range of board sizes. The non-attacking movement being limited to a wazir severely limits mobility, such that allowing faster movement along the edge of the board could be necessary to make it relevant in the midgame on a 12x12 board or larger. Even then, the centre of larger boards would be impossible to impact.
I'm not sure if it attacks as a leaper for the Dabbaba-attack, but I was imagining non-leaper (eg slides continuously 2 spaces cardinally when attacking at non-bishopric range-2). I think endowing it with knight movement (but not attack) would also be natural in some respects, since it makes the union of the attacking squares and moving squares forming a perfect 5x5 square centered on the piece (eg the union has the same coverage as a range-2 king). I'm amenable to this, since it is a natural way to empower the movement, however I'm also biased against it. Not only is adding knight-movement quite powerful, but I also think giving such movement to a piece such as this might reduce the specialness and flavour of knights themselves and many knight-like fairy chess pieces.
-- mid-range + mid-power
-- soft-confined to the edges of the board
The specifics I have in mind:
-- moves cardinally with a range of 1 (like a wazir)
-- attacks same-coloured squares within 2 tiles (a dabbaba + range-2 bishop) IF if it is at the edge of the board
Additionally for a much stronger, more relevant piece:
-- may attack if is adjacent to your own piece at the edge of the board
or even:
-- may attack if if connected to a chain of friendly pieces where at least one piece is at the edge of the board
The reason I'm interested in this piece idea is that generally fairy chess pieces are very powerful, and I think a natural way to limit the power of pieces whilst also allowing for interesting positions, would be to encourage their use near the edge of the board.
I'm on the fence about the "connected chain of pieces that touches the edge of the board", since on one hand that massively empowers this piece, but on the other hand only feels a bit "chesslike". Chess sees pawn chains, and pieces of heightened value within "logical chains" (dependencies of protection and attack within positions).