I am not sure but maybe you could chek the clathrin level as they are structural protein of certain vesicles or you can look for Notch which is a key receptor of endocytosis?

Well, you can check the endocytosis of well established EGFR, LDHR and transferrin receptors. If your stimulus is affecting  clathrin mediated pathway, then EGFR endocytosis will be prevented and you will observe more surface levels of EGFR or total EGFR levels as EGFR entry to lysosomes is now prevented or impeded. Moreover, you can also look for the expression of molecules which regulates or required for protein endocytosis such as Rab5A or dynamin.

Since you should want to distinguish only the fraction of a cargo that has been endocyted (not the protein in the plasma membrane nor along its synthesis route), I can think in two alternatives:

i) Biotinylation of surface proteins followed by separation of plasma membrane and intracellular vesicles by subcellular fractionation (centrifugation). Then you can calculate a ratio between surface-associated proteins and the intracellular membranes-associated ones. This ratio only can be altered by endocytosis.

ii) If you want to analyse a particular receptor (which endocytosis kinetics is well described, as EGFR or TfnR) you can immunostain surface proteins in live cells and after endocytosis to wash the remaining antibodies from the surface, as has been described in Chen Z-Y et al., 2005 (MBoC, 16:5761-5772). Although it was originally designed for microscopy, I guess the method may be easily adapted for being revealed by westernblot.

I hope you enjoy those experiments.  ;)

DON'T FORGET YOUR POSITIVE AND NEGATIVE CONTROLS.