Is it possible to wrap a dynamic object in an ELF dynamically linked binary?

I am attempting to wrap a glibc symbol with my own definition of that symbol. For functions that glibc exposes this has so far been as easy as defining a __wrap_function_name in my source code and then adding Wl,--wrap=external_function_name to the linker flags of my build system's linking steps. In practice this then would look something like:

extern "C" void __wrap_external_function_name(void) {    my_internal function();}

However I have recently attempted the same on a variable that glibc exposes, in this case __signgam. I again defined the linker flags for its wrapper, but I am not sure how and if it is even possible to define the wrapper for a variable. I attempted __wrap__signgam = signgam, but that had no effect. In fact the symbol table when exposed with objdump -T binary | grep signgam had the following content, showing that even though the wrap function is defined, the original symbol remains untouched:

0000000000000000      DO *UND*  0000000000000000  GLIBC_2.23  __signgam0000000000000000      DO *UND*  0000000000000000  GLIBC_2.2.5 signgam0000000001509d24 g    DO .bss   0000000000000004  Base        __wrap___signgam

Is there a canonical way to wrap these dynamic objects?