Conundrum really but nicely put.
Someone smarter than me will come along soon but i will have a crack at this for now.
It is relative. Time does exist for light but given its usage as a measure, you will need an alternative measure to gauge time re light. The problem with the science here and measure for us is mass. We cannot fathom massless entities let alone use them as a measure. It just dissolves quantum mechanics into theory. So, does light have mass or if not how does it have momentum? Gravity becomes problematic now. A real conundrum!!