Although tap water iontophoresis is most commonly used for hyperhidrosis, it has a long and successful history of use in eczema treatment as well. In particular, dyshidrotic eczema (also known as pompholyx or dyshidrosis) can be treated with iontophoresis as both an adjunct to topical corticosteriod treatment, and as a stand alone intervention.
As a stand alone intervention, 17 out of 20 patients in a split-body tap water iontophoresis trial showed improvement in their dyshidrotic excema symptoms, but only on the treated side, compared to a complete lack of improvement in the untreated side. 
When used in conjunction with topical corticosteriods, the time for clearance has been reported to be similar to high potency topical corticosteroids, but with the added benefit of a much increased remission time (average of 24.8 weeks vs 8.35 weeks). There have also been case reports of other combinations therapies, such as adding iontophoresis to patients treated with systemic or topical retinoids, phototherapy, or systemic immunosuppressants such as cyclosporine.
In terms of mechanism, there is a strong argument that aquaporins are involved in the pathology of dishydrodic excema. Likewise, there is some evidence that tap water iontophoresis has effects in the aquaporin pathway, in part by the reduction in skin pH shown in patients with successful hyperhidrosis treatment. 
Overall, tap water iontophoresis should be considered as an effective stand alone or add-on treatment.
 Odia, et al. Successful treatment of dyshidrotic hand eczema using tap water iontophoresis with pulsed direct current. Acta Dermatol Venereol. 1996;76:472–4.
 Wollina, et al. [Therapy of hyperhidrosis with tap water iontophoresis. Positive effect on healing time and lack of recurrence in hand-foot eczema].[Article in German]. Hautarzt. 1998 Feb;49(2):109-13.
 Soler, et al. The Key Role of Aquaporin 3 and Aquaporin 10 in the Pathogenesis of Pompholyx. Med Hypotheses. 2015 May; 84(5): 498–503.Published online 2015 Feb 11. doi: 10.1016/j.mehy.2015.02.006
 Nakahigashi, et al. Reduction of Skin pH during Treatment for Palmoplantar Hyperhidrosis: A Conjecture on the Role of pH-Regulated Water Channel, i.e. Aquaporin. Case Rep Dermatol. 2013 Jan-Apr; 5(1): 126–128. Published online 2013 Apr 18. doi: 10.1159/000348855