Can brain zaps be demonstrated by EEG? Brain zaps are explained as an electrical buzz in the head and the symptoms occur while withdrawing slowly from an SSRI antidepressant medication. 

Is it possible to detect brain zaps by placing EEG electrodes on the locations where many people report the phenomenon to occur (neck, spine, arms, ears, eyes, lips)?
Short answer
I haven't been able to find studies on EEG correlates of antidepressant discontinuation syndrome. 

Background
'Brain zap' is a colloquial term for antidepressant discontinuation syndrome.

Note that the sensations you mention in the arms, neck and lips etc are likely caused by central effects (i.e., in the brain) that evoke sensory perceptions as if they occur peripherally. Hence, any electrical activity associated with antidepressant discontinuation syndrome should, likely, be sought in the cortex.

I did a literature search on Antidepressant discontinuation syndrome AND EEG and I couldn't find anything. 

The EEG is classically used to detect gross disturbances in the brain, like epileptic activity. Epileptic discharges are paroxysmal events characterized by large parts of the cortex being synchronously entrained in activation. Because it is the cortex that is activated, the EEG electrodes are right on top of where the activity is and hence pick it up easily. Furthermore, the amplitude of epileptic EEG activity is very high compared to the normal background EEG (Fig. 1), because large parts of the cortex fire synchronously. The clinical symptomatology of epilepsy is hence expressed as gross changes in motor behavior (convulsions), loss of consciousness or other signs (Smith, 2005).

Those brain zaps are comparatively benign events: 


  Most cases of discontinuation syndrome last between one and four weeks, are relatively mild, and resolve on their own...  


(source: wikipedia)

Hence these 'zaps' may not pop out so easily above the background EEG. Further, epileptic discharges happen often, even in the absence of clinical symptomatologies, so they are picked up easily. Moreover, epileptic activity can often be provoked, for example by flashing a stroboscope in fron of the sufferer. Evoked activity can more easily be registered with EEG because the time window of interest is defined. Brain zaps on the other hand may be less common and the electrophysiologist would simply have to wait for them to occur. And even then, mild brain activity may not be sufficiently different from background EEG to yield a proper signal.   


Fig. 1. EEG of epileptic discharges show up clearly against the background EEG. source: Smith (2005)

Reference
- Smith, J Neurol Neurosurg Psychiatry (2005); 76(SII): ii2–7