Hello! Absolutely, I'd be thrilled to provide you with some tips for your forthcoming trip to Jeonju, Seoul, and Busan.

Best Time to Visit:
The best time to visit Jeonju, Seoul, and Busan is during the Spring (April-June) and Fall (September-November) seasons. During these times, the temperatures are moderate, and the country is particularly beautiful with cherry blossoms in Spring and colorful autumn leaves in fall.

Route and Accessibility:
Starting with Seoul, it's readily accessible from major cities around the globe. From Seoul, you can take a KTX train to Jeonju which takes approximately 2 hours. For Busan, you can use either the KTX high-speed train from Seoul, which takes about 3 hours, or from Jeonju, which takes around 2 hours.

Accommodation and Booking:
There are various accommodation options available in all three cities, ranging from luxury hotels to guesthouses. It's always advisable to book your accommodation in advance. Websites like Booking.com, Agoda, or Airbnb provide lots of choices.

Clothing and Essentials:
Pack lightweight clothing for summers, but for spring and autumn, carrying a light jacket or sweater is advised because it can be a bit chilly during mornings and evenings. For your winter visit, don't forget to pack warm clothing including boots, scarves, and gloves. Always carry essential travel documents, a power adapter (South Korea uses type C and F plugs), and personal sanitary products.

Health and Safety:
South Korea is generally quite safe. However, standard travel safety measures should always be adhered to like ensuring travel insurance, keeping personal belongings safe, and having local emergency contact numbers. Check the latest COVID-19 health travel advisory for your visit.

Local Etiquette and Respect:
South Koreans value respect and politeness. A bow is a common way to greet. It's quite common to remove shoes when entering someone's home and even some restaurants. Respecting local traditions and customs is always encouraged.