Can a basal cell carcinoma start out like a pimple and shrink down until only a red spot is left?

Basal cell carcinomas come in all size, shape, and colors. Typically lesions increase in size as the malignant cells multiply exponentially.  However, tumors like people, have temporary setbacks. The immune system may recognize and attack them. Topical chemicals and pressure may retard them.  They may out pace their circulation. There are many known and unknown rears for regression.The important thing is to get them, before they get you.  A simple biopsy will give a difinitive diagnosis and eliminate sleepless nights.  When in doubt, check it out.

Based on the location and what you are describing it might be quite possible that it's a BCC. Please make an appointment for an in-person exam and that person will do a biopsy if needed. "This answer has been solicited without seeing this patient and
cannot be held as true medical advice, but only opinion. Seek in-person
treatment with a trained medical professional for appropriate care."

The only way to know if you have a Basal Cell or Squamous Cell Carcinoma is with a biopsy.  I have seen them start the way you described.  Take care!  Dr. Z