make install calls /sbin/installkernel which will update the vmlinuz symlink. There is no option to disable this behavior. However, if you copy /sbin/installkernel to ~/bin/installkernel you can remove the linking from that copy and make install uses this location for installkernel in preference to /sbin/.
In my version of installkernel it is this part of the updatever function:
44 # This section is for backwards compatibility only
45 if test -f "$dir/$1" ; then
46 # The presence of "$dir/$1" is unusual in modern intallations, and
47 # the results are mostly unused. So only recreate them if they
48 # already existed.
49 if test -L "$dir/$1" ; then
50 # If we were using links, continue to use links, updating if
51 # we need to.
52 if [ "$(readlink -f ${dir}/${1})" = "${dir}/${1}-${ver}" ]; then
53 # Yup, we need to change
54 ln -sf "$1-$ver.old" "$dir/$1.old"
55 else
56 mv "$dir/$1" "$dir/$1.old"
57 fi
58 ln -sf "$1-$ver" "$dir/$1"
59 else # No links
60 mv "$dir/$1" "$dir/$1.old"
61 cat "$2" > "$dir/$1"
62 fi
63 fi
Personally, I don't use the vmlinuz and System.Map at all.