Congratulations on moving the probate along towards its conclusion. You are fortunate to have some siblings willing to help you with the process of organizing and selling the personal property.
Whether or not you are required to give Notice of Proposed Action is not dependent upon whether everyone knows about it. If you were granted authority under the Independent Administration of Estates Act by the court, you, as the personal representative, can take certain actions that do not require court supervision authority only after giving a notice of proposed action to the affected parties. Selling the personal property at an estate sale does not require such notice. However, you should give the proposed action notice before making a preliminary distribution of the personal property (Prob Code §10520). Since it sounds as though you will be distributing personal property as bequeathed under the will, you should know that such actions taken before an order for distribution are considered to be preliminary distributions and are authorized only if the time for filing creditors' claims has expired, and it appears that the distribution may be made without loss to creditors or injury to the estate or any interested person.
Also the preliminary distribution of any household furniture and furnishings, motor vehicles, clothing, jewelry, and other tangible articles of a personal nature to those siblings, and you, who are entitled to this property under decedent's will, cannot have a total fair market value of more than $50,000.
You are only required to give the notice. The Judicial Council form has a place for a beneficiary or interested party to consent or object to the notice. However, there is no requirement that the beneficiary respond. I’m not sure what you mean by your questions as to whether the nonparticipating sibling is not receptive to the notice. Again, you only have to mail the notice to him or her.
Disclaimer: The above answer does not create an attorney/client relationship. My responses are intended to provide general information about the question posted. I am licensed to practice in the state of California. The information provided on this site should not be used as a substitute for conferring with or hiring a competent legal advice from a licensed attorney that practices in the subject area in your state.
Notice of Proposed Action is necessary whenever you change the form of any assets, usually by selling. It is recommended you always give notice to protect yourself. When you sell real property, it is always required.