E.g. Contac 600 Plus can be found in basically all drug stores and it has 120mg of Pseudoephedrine, 100mg Caffeine, 8mg Chlorpheniramine, and 0.4mg of Belladonna Extract. It sounds like it'll actually be illegal to import into Japan, since 120/(120 + 100 + 8 + 0.4) is over 10%, but I've previously just walked into a drug store and bought a packet.
But, it's not unheard of to get randomly stopped by the police and searched, especially in touristy areas like train stations. Unless you're a Japanese citizen, you have to show ID, and although the searches are optional, most people agree to them.
For customs, usually a few people from each plane are searched.
Anecdotally, if you're a tourist, they're usually looking for medicine that was legal outside of Japan, but illegal within Japan, with small amounts leading to being detained for 23 days (like in this blog post). And if they decide to prosecute you, you'd probably get a suspended sentence (so no prison time), but you'd get deported and a temporary ban from coming back to Japan.
For what it is worth different countries have vastly different recommendations for HBP and these drugs. I recommend discussing with the pharmacists in your country.
In the US I have been told it's a strict "never", in Ireland I was told that it wouldn't have a measurable effect on blood pressure. I've also measured my personal blood pressure (pre-hypertension to stage 1) and have not been able to measure a difference in blood pressure.
