"Neurogenic rosacea was first described by Scharschmidt et al. in 2011, and since then, there have been very few reports of its existence. It is characterized by dramatic facial redness, with burning, stinging and dysaesthesia that is out of proportion to the flushing or inflammation. A relatively high number of patients have neurological or neuropsychiatric conditions, including complex regional pain syndrome, essential tremor, depression and obsessive compulsive disorder. Treatment is difficult, and a poor response is typically seen with standard treatments used in rosacea. Some success has been seen with neuroleptic agents (e.g. pregabalin, gabapentin), tricyclic antidepressants and duloxetine. Endoscopic thoracic sympathectomy has also been used with some success in treating debilitating facial flushing." 
The above article discusses a patient with neurogenic rosacea that was treated with pregabalin (Lyrica) and states the following:
"The patient could not tolerate gabapentin, but within 2 months of starting pregabalin, her symptoms improved dramatically, with a reduction in facial burning sensation, redness and swelling. She is currently being maintained on pregabalin 300 mg in the morning and 225 mg at night." 
"We propose that this group of patients with strikingly prominent neurologic symptoms represents an under recognized subgroup of rosacea that we term neurogenic rosacea. By highlighting and formally naming this subgroup, we hope to increase awareness and recognition of these patients and aid the practicing dermatologist in their therapeutic management" 
The main difference between Neurologic Rosacea and Subtype 1, ETR, is the patient exhibits some additional neurologic or neuropsychiatric symptoms or signs such as headaches, depression, anxiety, Raynaud phenomenon, migraines, chronic pain and regional pain syndrome.
David Pascoe has an excellent article on treatments for this subtype and another interesting follow up on this with an article entitled, Neuropeptide PACAP Modulators for Neurogenic Rosacea.
An interesting statement in the article worth mentioning is this:
"Because our understanding of this enigmatic subclass of rosacea is extremely limited, further research is clearly needed to better describe the underlying pathophysiologic characteristics and to identify additional effective treatment methods." 
"Fourteen of 17 patients (82.3%) improved after receiving anticonvulsants and antidepressants. In conclusion, rosacea patients with severe neurological symptoms show distinct clinical manifestations and should be classified separately, and a different therapeutic approach is necessary for them." 
The British Association of Dermatologists journal describes 'neurogenic rosacea, a distinct variant of rosacea." 
laser_cat has a post about her experience with Neurogenic Rosacea.
Ange4 also suffers from Neurogenic Rosacea, so laser_cat responds to her request for help in this thread.
Confusion with Neuropathic Rosacea
Neurogenic Rosacea should not be confused with Neuropathic Rosacea, however it is confusing, which is another proposed subtype, similar, but has not gained a wider acceptance as the term to use. The two names are similar as well as the description of the signs/symptoms but there is not a consensus on either distinguishing these two terms or in clarifying them among 'authorities.' It may be possible that these two terms may be describing the same condition.
Other than the treatment mentioned in the cited articles here are some other treatments to consider:
laser_cat at RF who suffers from neurogenic rosacea posts that amlodipine has helped in her struggle and lists other drugs she is taking to fight this. 
"Interestingly, hydroxychloroquine, an antimalarial medication and disease-modifying antirheumatic drug (DMARD), demonstrated effectiveness in treating symptoms in a subgroup of the neurogenic rosacea patients."
Neurogenic Rosacea: What Pharmacists Should Know, Pharmacy Times
In conclusion, the differentiating factor for neurogenic rosacea is mentioned in the article:
"A notably high percentage of patients had neurologic (43% [6 of 14]) or neuropsychiatric (50% [7 of 14]) conditions, including complex regional pain syndrome, essential tremor, depression, and obsessive-compulsive disorder. Neurovascular disorders, including headaches (71% [10 of 14]) and Raynaud phenomenon (29% [4 of 14]), as well as rheumatologic disorders (36% [5 of 14]), including lupus, rheumatoid arthritis, fibromyalgia, mixed connective tissue disease, and psoriatic arthritis, were also common." 
The article proposed the following:
"We propose that this group of patients with strikingly prominent neurologic symptoms represents an underrecognized subgroup of rosacea that we term neurogenic rosacea. By highlighting and formally naming this subgroup, we hope to increase awareness and recognition of these patients and aid the practicing dermatologist in their therapeutic management."
It would be pertinent to differentiate erythromelalgia (EM) from Neurogenic Rosacea in a differential diagnosis.
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 Clin Exp Dermatol. 2015 Dec;40(8):930-1. doi: 10.1111/ced.12630. Epub 2015 Mar 2.
Neurogenic rosacea: an uncommon and poorly recognized entity?
Parkins GJ, Maan A, Dawn G.
 Neurogenic Rosacea: A Distinct Clinical Subtype Requiring a Modified Approach to Treatment
Tiffany C. Scharschmidt, MD; John M. Yost, MD, MPH; Sam V. Truong, MD; Martin Steinhoff, MD, PhD; Kevin C. Wang, MD, PhD; Timothy G. Berger, MD
Arch Dermatol. 2011;147(1):123-126. doi:10.1001/archdermatol.2010.413
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Neurogenic rosacea in Korea.
Kim HO, Kang SY, Kim KE, Cho SY, Kim KH, Kim IH