I had a quick look at resolv.conf's manpage on Debian and I think @daddy32's suggestion of adding a second nameserver would actually work:
nameserver Name server IP address
Internet address of a name server that the resolver should query, either an IPv4 address (in dot notation), or an IPv6 address in colon (and possibly dot) notation as per RFC 2373. Up to MAXNS (currently 3, see <re‐
solv.h>) name servers may be listed, one per keyword. If there are multiple servers, the resolver library queries them in the order listed. If no nameserver entries are present, the default is to use the name server
on the local machine. (The algorithm used is to try a name server, and if the query times out, try the next, until out of name servers, then repeat trying all the name servers until a maximum number of retries are
made.)
According to the doc, the resolver will try each name server in order until one is successful.