Claim: When Metaclass I factorises into a double light cone, the null cone intersection is two lines.

Define Lorentz null cones

AA= (({{1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, (1/2) (-D3+(Sqrt[-4+(D3^2)])), 0}, {0, 0, 0, (1/2) (-D3+(Sqrt[-4+(D3^2)]))}}));
BB = (({{1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, (1/2) (-D3-(Sqrt[-4+(D3^2)])), 0}, {0, 0, 0, (1/2) (-D3-(Sqrt[-4+(D3^2)]))}}));

Suppose v is a null vector for both Lorentz metrics

v={a0,a1,a2,a3}

p0=v.AA.v;
p1=v.BB.v;

If p0 = 0 and p1 = 0, then it follows that p0-p1 = 0.

Simplify[p0-p1]

It follows that a2=a3=0

Simplify[(p0+p1)/.{a2->0,a3->0}]

It follows that a0= +/- a1

Check

vec={t,s,0,0};

vec.AA.vec
vec.BB.vec