Linking clinical narratives to standardized vocabularies and coding systems is a key component of unlocking the information in medical text for analysis. However, many domains of medical concepts lack well-developed terminologies that can support effective coding of medical text. We present a framework for developing natural language processing (NLP) technologies for automated coding of under-studied types of medical information, and demonstrate its applicability via a case study on physical mobility function. Mobility is a component of many health measures, from post-acute care and surgical outcomes to chronic frailty and disability, and is coded in the International Classification of Functioning, Disability, and Health (ICF). However, mobility and other types of functional activity remain under-studied in medical informatics, and neither the ICF nor commonly-used medical terminologies capture functional status terminology in practice. We investigated two data-driven paradigms, classification and candidate selection, to link narrative observations of mobility to standardized ICF codes, using a dataset of clinical narratives from physical therapy encounters. Recent advances in language modeling and word embedding were used as features for established machine learning models and a novel deep learning approach, achieving a macro F-1 score of 84% on linking mobility activity reports to ICF codes. Both classification and candidate selection approaches present distinct strengths for automated coding in under-studied domains, and we highlight that the combination of (i) a small annotated data set; (ii) expert definitions of codes of interest; and (iii) a representative text corpus is sufficient to produce high-performing automated coding systems. This study has implications for the ongoing growth of NLP tools for a variety of specialized applications in clinical care and research.