Identifying reputable journal indexing services
I think that there is a critical distinction to be made here between defining reputable indexing services and identifying such services.

I suspect that for most well-established scholars, it is relatively straightforward to identify whether an indexing service is reputable or not. For example, if you talk to a computer scientist, they'll point to DBLP, MathSciNet is a good one for mathematicians as noted in the comments, and PubMed is good for life sciences.  Random predatory anything is usually pretty easy to determine with a little bit of research.

In order to define "reputable indexing service" for the sake of policy, then, I would suggest that it is likely to be effective to have a process by which faculty members can request an index be considered and then a few internal and external experts in the field are asked to certify whether the index is reputable or not.  That way, there's not a formal definition enshrined in policy that might be evaded by technicalities, but instead some human judgement is involved.