When fine-tuning language models on new tasks, catastrophic forgetting -- performance degradation on previously-learned tasks -- is a ubiquitous problem. While Parameter-Efficient Fine-Tuning (PEFT) methods like LoRA address this through low-rank adapters, sparse adaptation offers an alternative that doesn't impose rank constraints. We introduce Random Initialization of Gated Sparse Adapters (RIGSA), which starts from randomly-initialized full-rank adapters, gates them with a ReZero analog, and sparsifies them with iterative magnitude pruning. We evaluate RIGSA on SmolLM2-1.7B-Instruct using a novel vision-in-text task (Textual MNIST) and measure forgetting on PIQA, HellaSwag, and GSM8k. SmolLM2-1.7B-Instruct initially performs around chance level on Textual MNIST, and is capable of learning the task through RIGSA, 4-bit QLoRA and random masking. In spite of having more trainable parameters than QLoRA, the RIGSA configurations that we studied displayed less forgetting than QLoRA, particularly on GSM8k, though it performs comparably to random masking.