Graphic Processing Units (GPUs) are promising solutions in safety-critical applications, e.g., in the automotive domain. In these applications, reliability and functional safety are relevant factors. Nowadays, many challenges are impacting the implementation of high-performance devices, including GPUs. Moreover, there is the need for effective fault detection solutions to guarantee the correct in-field operation. This work describes a modular approach to develop functional testing solutions based on the non-invasive Software-Based Self-Test (SBST) strategy. We propose a scalar and modular mechanism to develop test programs based on schematic organizations of functions allowing the exploration of different solutions using software functions. The FlexGripPlus model was employed to evaluate experimentally the proposed strategies, targeting the embedded memories in the GPU. Results show that the proposed strategies are effective to test the target structures and detect from 98% up to 100% of permanent stuck-at faults.