The Icare tonometer will give you an accurate reading almost immediately after you complete punctal occlusion.
However, if you are asking how long until the beta blocker eye drop shows some efficacy in lowering your IOP, it will be approximately 20 minutes. It will be a couple hours before you see peak efficacy.
Responses to a beta-blocker are highly variable among patients. Results of numerous studies show that genetic polymorphisms contribute to variability in responses to beta-blockers.
Most beta-blockers show peak concentrations about 1-3 hours after ingestion. The half lives of beta-blockers are variable, but most have a half life of 3-10 hours. Most beta-blockers are metabolised by the liver.