This is a new area, but the research that has come out since this article is also positive, and promising. One example: In this June 2018 study of 23 people with obesity, 12 weeks of 8-hour time-restricted feeding resulted a 2.6% decrease in body weight and a 7 point decrease in systolic blood pressure, which was significant when compared to controls: https://www.ncbi.nlm.nih.gov/pubmed/29951594
So does that mean you should abstain from your caffeine fix when fasting? According to Dr. Josh Axe, D.N.M., C.N.S., D.C., founder of DrAxe.com, bestselling author of Eat Dirt, and cofounder of Ancient Nutrition, tea and coffee are fine to consume as long as you don't add any milk or sweeteners. He explains on his blog, "If you're on a time-restricted fast and you're in no-eating hours, it's best to stick to no- or low-calorie drinks like water, coffee, (with no milk) and tea. If you're on an alternate day diet or something similar, even during low calorie hours, you can technically drink whatever you'd like — but remember, this will count against your calories." Dr. Palanisamy also agrees that during fasting, the "appetite-suppressing effects of coffee are probably beneficial."
One monk, for example, set out to do a 40 day fast with medical supervision while maintaining his daily activities in the monastery. After 36 days, the medical professionals had to step in due to “profound weakness” and low blood pressure when standing. Although the monk fasted for 15 days longer than Ghandi, the medical professionals were able to stop the fast in time so that he could recover.
There were [no statistical] differences between the low- and high- [meal frequency] groups for adiposity indices, appetite measurements or gut peptides (peptide YY and ghrelin) either before or after the intervention. We conclude that increasing meal frequency does not promote greater body weight loss under the conditions described in the present study.