How to nicely make a neighbors discovery solicitation on Linux?
ndisc6 -1 fe80::1234 eth0
eth0 with the correct interface name, of course.
Due to your requirement for this to be reflected in the kernel's neighbors, and your reluctance to install software, try ICMP echo:
ping -c 1 fe80::1234%eth0
Does not really matter what protocol you attempt, so long as it is IP based.
If you are willing to install software, nmap has discovery features. Here is a NDP only scan, output to a XML file (and stdout) which includes the link layer address:
nmap -sn -PR -oX /tmp/lladdr.xml -6 fe80::1234%eth0
Apparently, this type of nmap scan tickles the kernel to do neighbor discovery, as in testing I see it reappear under