I'm really not sure what you're asking when you say "gaiting"...I assume you mean making a patient walk so you can ascertain their "gait?"
There are some old-fashioned/classic rules about this, but really no guarantees. Dizzy patients don't like to play by the rules.
The four basic categories for dizziness are: Caridac, Peripheral, Central, and Other. An example of a classic rule related to these four categories is the patient complaint of lightheadedness being theoretically more suggestive of a cardiac etiology as compared to a peripheral nervous system etiology.
Classically, someone who complains of dysequilibrium is that CNS-induced dizzy patient, and the patient complaining of subjective or objective vertigo is the PNS-induced dizzy patient. Classically, a CNS lesion (as opposed to a peripheral one) should result in their gait being *somehow* affected (if they can walk at all). A peripheral lesion shouldn't really be affecting their ability to walk as much as a central lesion. But yeah, PNS-dizziness could certainly affect gait (if pronounced enough) and CNS-dizziness might not affect gait. So as a general rule it's a fair statement to keep in mind, but I wouldn't think of gait as a guarantee.
You'll find that there is a lot of symptomatic overlap with these guys/gals, and another complicating problem is that they are often very suggestive patients who endorse any characteristics of dizziness when asked.
Basically, I believe you should be checking gait in any dizzy patient who you think has ANY neurologic syndrome. It goes along with testing their arms and legs for dysmetria and ataxia, and looking for nystagmus.