That is a very difficult problem worth a PhD project in physical chemistry. Intially, I thought one could try capillary electrophoresis at different pHs and if the analyte travels with the electrosmotic flow marker at a certain pH, one can say a zwitterion has existed (or a neutral form) by inference. However, you query is about distinguishing the neutral state and the zwitterionic state. One has to think about spectroscopic techniques that rely on dipole moments. Since you are interested in aqueous phase, gas phase microwave spectroscopy of amino-acids is out of question (there are papers on it). Since zwitterion ions can possess large dipole moments as compared to their neutral counterparts, two remaining ones are infrared and photoelectron spectroscopy.
Zwitterion formation in hydrated amino acid, dipole bound anions: How many water molecules are required? J. Chem. Phys. 119, 10696 (2003); https://doi.org/10.1063/1.1620501
We utilize the facts that zwitterions possess very large dipole
moments, and that excess electrons can bind to strong dipole fields to
form dipole bound anions, which in turn display distinctive and
recognizible photoelectron spectral signatures. The appearance of
dipole-bound photoelectron spectra of hydrated amino acid anions,
beginning at a given hydration number, thus signals the onset of
greatly enhanced dipole moments there and, by implication, of
zwitterion formation.
IR would be finiky with water, but there are reports that water bound to zwitterions has a different vibrational frequency
Stability and IR Spectroscopy of Zwitterionic Form of β-Alanine in Water Clusters, J. Phys. Chem. B 2019, 123, 20, 4392–4399, https://doi.org/10.1021/acs.jpcb.9b00654
We perform an experimental and computational study on the number of
water molecules needed for zwitterion formation of β-alanine. Our
density functional theory investigation reveals that a minimum of five
water molecules are required to form and stabilize the zwitterion. A
characteristic connecting water molecule located between the COO– and
NH3+ groups is found to enhance the stability. This water molecule is
also involved in a characteristic infrared active vibration at ≈1560
cm–1, which is slightly shifted with the number of surrounding water
molecules and is located in a spectral region outside of water
vibrations.
