Namespace Configuration

    Friend Class DbConnectionHelper

        Friend Shared Function ConnectionString() As String

            Dim sqlbuilder As New SqlClient.SqlConnectionStringBuilder

            sqlbuilder.DataSource = "Имя sql сервака"
            sqlbuilder.InitialCatalog = "Имя дата базы"

            sqlbuilder.UserID = "login"
            sqlbuilder.Password = "password"

            sqlbuilder.PersistSecurityInfo = True
            sqlbuilder.MultipleActiveResultSets = True
            sqlbuilder.ApplicationName = "EntityFramework"

            Return sqlbuilder.ConnectionString

        End Function

        Friend Shared Function ConnectionStringLocalDb() As String

            Dim sqlbuilder As New SqlClient.SqlConnectionStringBuilder

            sqlbuilder.DataSource = "(localdb)\ProjectsV12"
            sqlbuilder.InitialCatalog = "Имя дата базы"

            sqlbuilder.IntegratedSecurity = True
            sqlbuilder.ConnectTimeout = 30
            sqlbuilder.Encrypt = False
            sqlbuilder.TrustServerCertificate = False

            sqlbuilder.ApplicationIntent = SqlClient.ApplicationIntent.ReadWrite
            sqlbuilder.MultiSubnetFailover = False

            sqlbuilder.ApplicationName = "EntityFramework"

            Return sqlbuilder.ConnectionString

        End Function
    End Class

End Namespace

PS. Смотрите конфиг. Я не смог реализовать Section но вроде работает и так ))
PS.S. Если у вас 2 и более базы данных в проекте то конфиг для них должен быть один (по моему так).

Public Class DbConfigurationHelper
    Inherits System.Data.Entity.DbConfiguration

    Friend Sub New()
        SetProviderServices(Entity.SqlServer.SqlProviderServices.ProviderInvariantName, Entity.SqlServer.SqlProviderServices.Instance)
        SetDefaultConnectionFactory(New Entity.Infrastructure.LocalDbConnectionFactory("mssqllocaldb"))
    End Sub

<DbConfigurationType(GetType(DbConfigurationHelper))>
Partial Public Class DbContextNameDatabase
    Inherits DbContext

    Public Sub New()
        MyBase.New(DbConnectionHelper.ConnectionString)
    End Sub

End Class

Friend Shared Function ConnectionStringDev() As String
Friend Shared Function ConnectionStringTest() As String
Friend Shared Function ConnectionStringPrelive() As String
Friend Shared Function ConnectionStringLive() As String

<DbConfigurationType(GetType(DbConfigurationHelper))>
Partial Public Class DbContextNameDatabase
    Inherits DbContext
    Public Sub New()
        MyBase.New(DbConnectionHelper.ConnectionStringLive)
    End Sub
End Class