Decades ago, I remember figuring out quite a bit of that, and here are my original notes from that, including tables that show the pattern clearly:

    MOV rA, rB:
         B: AL AH BL BH CL CH DL DH
    A:      1  1  0  0  1  1  0  0
    AL  1   ** ** 8A 8A ** ** 8A 8A
    AH  1   ** ** 8A 8A ** ** 8A 8A
    BL  0   8A 8A ** ** 8A 8A ** **
    BH  0   8A 8A ** ** 8A 8A ** **
    CL  1   ** ** 8A 8A ** ** 8A 8A
    CH  1   ** ** 8A 8A ** ** 8A 8A
    DL  0   8A 8A ** ** 8A 8A ** **
    DH  0   8A 8A ** ** 8A 8A ** **

    * = "reversed" opcode (88)

    MOV rA, rB ( word regs ):
         B: AX BX CX DX SP BP SI DI
    A:      1  0  1  0  1  1  0  0
    AX 1    ** 8B ** 8B ** ** 8B 8B
    BX 0    8B ** 8B ** 8B 8B ** **
    CX 1    ** 8B ** 8B ** ** 8B 8B
    DX 0    8B ** 8B ** 8B 8B ** **
    SP 1    ** 8B ** 8B ** ** 8B 8B
    BP 1    ** 8B ** 8B ** ** 8B 8B
    SI 0    8B ** 8B ** 8B 8B ** **
    DI 0    8B ** 8B ** 8B 8B ** **

    * = "reversed" opcode (89)

    The above tables apply for the following two-operand instructions:

        ADD             OR
        ADC             SBB
        AND             SUB
        XOR             CMP

    For TEST and XCHG, which are commutative, A86 always puts the first
    operand in the r/m field if possible, while MASM puts it in the reg
    field if the first operand is a register.