Cough is a common symptom of multiple respiratory diseases, such as asthma and chronic obstructive pulmonary disorder. Various research works targeted cough detection as a means for continuous monitoring of these respiratory health conditions. This has been mainly achieved using sophisticated machine learning or deep learning algorithms fed with audio recordings. In this work, we explore the use of an alternative detection method, since audio can generate privacy and security concerns related to the use of always-on microphones. This study proposes the use of a non-contact tri-axial accelerometer for motion detection to differentiate between cough and non-cough events/movements. A total of 43 time-domain features were extracted from the acquired tri-axial accelerometry signals. These features were evaluated and ranked for their importance using six methods with adjustable conditions, resulting in a total of 11 feature rankings. The ranking methods included model-based feature importance algorithms, first principal component, leave-one-out, permutation, and recursive features elimination (RFE). The ranking results were further used in the feature selection of the top 10, 20, and 30 for use in cough detection. A total of 68 classification models using a simple logistic regression classifier are reported, using two approaches for data splitting: subject-record-split and leave-one-subject-out (LOSO). The best-performing model out of the 34 using subject-record-split obtained an accuracy of 92.20%, sensitivity of 90.87%, specificity of 93.52%, and F1 score of 92.09% using only 20 features selected by the RFE method. The best-performing model out of the 34 using LOSO obtained an accuracy of 89.57%, sensitivity of 85.71%, specificity of 93.43%, and F1 score of 88.72% using only 10 features selected by the RFE method. These results demonstrate the ability for future implementation of a motion-based wearable cough detector.