The application of data-driven remaining useful life (RUL) prediction has long been constrained by the availability of large amount of degradation data. Mainstream solutions such as domain adaptation and meta-learning still rely on large amounts of historical degradation data from equipment that is identical or similar to the target, which imposes significant limitations in practical applications. This study investigates PEFT-MuTS, a Parameter-Efficient Fine-Tuning framework for few-shot RUL prediction, built on cross-domain pre-trained time-series representation models. Contrary to the widely held view that knowledge transfer in RUL prediction can only occur within similar devices, we demonstrate that substantial benefits can be achieved through pre-training process with large-scale cross-domain time series datasets. A independent feature tuning network and a meta-variable-based low rank multivariate fusion mechanism are developed to enable the pre-trained univariate time-series representation backbone model to fully exploit the multivariate relationships in degradation data for downstream RUL prediction task. Additionally, we introduce a zero-initialized regressor that stabilizes the fine-tuning process under few-shot conditions. Experiments on aero-engine and industrial bearing datasets demonstrate that our method can achieve effective RUL prediction even when less than 1\% of samples of target equipment are used. Meanwhile, it substantially outperforms conventional supervised and few-shot approaches while markedly reducing the data required to achieve high predictive accuracy. Our code is available at https://github.com/fuen1590/PEFT-MuTS.