Context. Observations of molecular clouds, prestellar cores, and protoplanetary disks have established that the HNC/HCN ratio may be a potent diagnostic of molecular gas physical conditions. The processes that govern the relative abundances of these molecules nevertheless remain poorly understood. Aims. We seek to exploit the wide range of UV irradiation strengths within the ∼pc diameter Helix planetary nebula to explore the potential role of UV radiation in driving HNC/HCN. Methods. We performed IRAM 30 m and APEX 12 m radio line observations across six positions within the Helix Nebula, making use of radiative transfer and photodissociation modeling codes to interpret the results for line intensities and line ratios in terms of the molecular gas properties. Results. We have obtained the first detections of the plasma-embedded Helix molecular knots (globules) in HCN, HNC, HCO+, and other trace molecules. Analysis of the HNC/HCN integrated line intensity ratio reveals an increase with radial distance from the Helix central star. In the context of molecular line ratios of other planetary nebulae from the literature, the HNC/HCN ratio appears to be anticorrelated with UV emission over four orders of magnitude in incident flux. Models of the photodissociation regions within the Helix using the RADEX and Meudon codes reveal strong constraints on the column density (1.5–2.5 × 1012 cm−2) of the molecular gas, as well as pressure and temperature. Analysis of the molecular ion HCO+ across the Helix indicates that X-ray irradiation is likely driving HCO+ production in the outer regions of planetary nebulae, where photodissociation is limited but cold gas and ionized molecules are abundant. Conclusions. Although the observational results clearly indicate that UV irradiation is important in determining the HNC/HCN ratio, our photodissociation region modeling indicates that the UV flux gradient alone cannot reproduce the observed variation in HNC/HCN across the Helix Nebula. Instead, HNC/HCN appears to be dependent on both UV irradiation and gas pressure and density.