Just a thought from an old clockwinder
In order to not have heading mode with an ILS mode you must first capture the ILS (LOC)same is true for V/S mode you must first capture G/S.
Alternativley if you are in HDG mode and select LNAV there is no delay as the flt plan can be adopted immediately, ie there are no external radio signals to intercept and track. So the HDG light go off immediately.