Monitoring human biosignals like electrocardiograms (ECG) and electroocculargrams (EOG) is of great interest to medicine, health, and wellness. Long-term recording of these biosignals is still challenging. This is because it relies on the use of electrolytes that are aqueous-based, and prone to evaporation or leaking, which can lead to inaccurate measurements after extended period, and/or causes discomfort to the user. In this work, we propose the use of a deep eutectic solvent gel electrolyte (eutectogel) as a replacement for conventional electrolytes to achieve low electrode-skin impedance during ECG and EOG measurements. This gel exhibits low volatility and has comparable impedance over a frequency range of 4 Hz to 8 MHz compared to two commercially available electrode gels, but uniquely does not increase impedance when left in ambient condition over several days. This low volatility can endow long-term real-time continuous measurements of electrogram recordings without the need to replace or monitor the electrode gel. This paper also reports a new class of flexible copper-fabric-based electrode with eutectogel for long-term recording of ECG and EOG.