All the literature on reflections in minkowski space, that I have found, have defined ways to reflect about an arbitrary planes or lines and they always add the disclaimer eventually that the plane or line one wishes to reflect with must be NOT lightlike.
For example, the formula that is utilized in general and I have seen be used for the minkowski inner product is
Ref($v$) = $v$ - $2\frac{<p,v>}{<p,p>}p$.
We see that this formula works ... but if we let $p$ move closer and closer to a lightlike vector we see the formula blows up $(<p,p> \rightarrow 0)$ and if we let $p$ be lightlike $(<p,p>= 0)$ it doesn't follow all standard properties of what it means to be a reflection (view comes Euclidean properties). After this formula is used, with the exclusion of reflection about lightlike planes and lightlike lines, authors will continue and prove many things but ignore or never state that formula contains ALL reflections and what a reflection about a lightlike object would be.
Main question: Does this formula, in Minkowski space, cover all possible reflections even though it excludes reflections about lightlike planes or lightlike lines? What should be done for that case when considering the exclusion ... (just say it is not possible and doesn't exist)?